Before we get to that, let me tell you why this trailer spurred me to talk about it, starting with a bit of background on the Pokémon games. The basic premise of the games (for those who have been living in the Mongolian jungles for the past twenty years) is that you play as a child who lives in a world inhabited by creatures called — you guessed it — Pokémon. You can catch these Pokémon in a device called a Pokéball, train them, and use them to fight other Pokémon trainers, and it’s your job to go off on an adventure to become the Pokémon Champion.

Woof! — Image Source

The games have always been primarily free-form. While the general path was set for you — you had to beat the eight Gym Leaders, and work your way to the Elite Four, running afoul of some evildoers along the way — it’s your choice on how to go about it. Want to catch a small team of Pokémon and raise them diligently? You can. Want to catch every species you see and expand your collection? You can. Want to change and train a new team for each new situation? You can. Want to blitz through the game with nothing but a team of six useless carp? You can, if you can manage it.

This is a more skilled player than I.

The charm of the games came down to the world and the freedom you were given within it. The worlds were expansive, giving you plenty to do even after the main storyline was complete. You could try and catch every species of Pokémon, of which there are hundreds. You could link up with your friends, trading to fill in gaps in your collection, or battling to see which of you was the strongest. You could explore ancient ruins and mysterious caves, fight and capture powerful beasts spoken of only in legends.

The basis in mythology and adventure was a big driving force for the games’ sense of wonderment. — Image Source

More than anything else, this was, and still is, a very resilient series. This was the series that got me into gaming back in the late 90s and early 2000s, and it’s still going strong in the midst of a struggling games industry. A large part of this was the series’ willful rejection of the trends of gaming in general — instead of aiming for cinematic spectacle, an epic story, and strong visual fidelity, the games kept themselves deliberately conservative, keeping the story skeletal, the technology simple, and the cinematics nearly non-existent. This allowed a greater focus on what really mattered — the design and expansiveness of the world and the multitude of creatures in it. There were some spin-offs which pushed the series in other directions, but the main series never changed much of the core formula. Even when 3D was adopted, it was adopted gingerly, keeping the art style and overhead view the same.

And it’s with good reason they do this. These trends have brought ruin on several of gaming’s most classic series. The Legend of Zelda series has moved away from an action-focused exploration game to a game focused more around simplistic puzzles with greater emphasis on narrative, and its sales have plummeted. The Metroid series was single-handedly destroyed by Metroid: Other M, which took a series based around exploration of a alien world through a silent protagonist who was a bad-ass bounty hunter, and turned it into a soap opera where the not-so-bad-ass bounty hunter explores her maternal instincts while being subordinate to a man. Final Fantasy, probably the worst offender of the lot, took an RPG series with a simple plot, expansive worlds, and rich mythological background, and made it linear, taking away exploration and freedom, in favor of story and character development. Final Fantasy, one of the most popular game series back in the day, is now irrelevant to modern gaming.

Why do game developers do this? I suspect it’s in a misguided search for sophistication and respect. The temptation for the game developers to regard themselves as “creative geniuses” pushes them to value their own imagination above the player’s, and this inevitably means creating more elaborate art, generally at the expense of the expansiveness of the world, limiting a player’s freedom, their ability to shape their own stories, in favor of the story the designers have set up for them, and developing elaborate characterization which restricts player autonomy (Tadhg Kelly said it best: there is no such thing as a player character). This ends up destroying the very things that made the series successful in the first place.

Pokémon has generally been able to resist these temptations up to this point. But even in the last released set of games, Pokémon Black and White, there are some troubling signs that they may be falling into the same trap. There was a greater emphasis on story. It spent more effort on character development, spending time talking about the antagonist’s and rivals’ life and struggles. The obstacles that kept you from progressing were more forced and contrived — rather than being a rock or tree or lake in the way of the next town, it was often just a person saying “you can’t go that way” who would only move when the story deemed it appropriate. There were several areas of the game which served no purpose other than showing off the fancy 3D features. Even the world map seemed more artificial in comparison to the natural landscapes of previous games.

And then came this trailer, for the direct, story-based sequels to Black and White, Black 2 and White 2.

Now don’t be fooled. This is, in fact, a trailer for the new game, despite the fact that it looks like a trailer for one of the associated movies or TV shows. And yet, it shows nothing of the game itself, focusing instead on the characters and story. Compare it with this trailer for Pokémon Platinum, released back in 2009, which is focused entirely on the game itself.

Taken alone, each of these signs wouldn’t be too alarming. But when brought together, it shows a series at risk of falling into the trap of “creative genius”. We’ll have to wait and see what happens, but should my suspicions prove true, we risk losing one of the last bastions of true gaming.

It took over a year, but I’ve finally followed through that suggestion. I’ve cleaned it up slightly from its initial version, but for the most part the content is similar to the original Reddit comment.

What is light, anyway?

Let’s start with the initial question — light, is it a particle, or a wave? As it turns out, light exhibits properties of both. Let’s take these two ways of seeing light individually. I’m going to take this painfully slowly, so feel free to skip some of this stuff if you already know it.

Light as a wave

I’m hoping everyone here knows what interference is. If you don’t, take a look at the image below:

Interference of two waves — Image source

On either side, you have two smaller waves at the bottom, and the one on the top is what you get when you add them up. Depending on how “in-sync” the two waves are (their phase), you could end up with a wave that’s twice as big (“constructive interference”), or the two waves could cancel each other out (“destructive interference”), or you could get anything in between. It turns out that light behaves in exactly this way, and the classic example of this is the double-slit experiment.

If you shine light at a small slit, it makes a nice round wave that looks a lot like ripples in a pond. This is due to a phenomenon called diffraction, which is found in things like water as well — if you have a flat wave coming at an obstacle with a slit in it, the wave “bends” around the corners of the obstacle and creates something that’s roughly circular, if your slit is small enough, as in the image below:

Diffraction of a wave — Image source

Light does this as well. If you shine a light at a small enough slit, you end up with a spread-out sort of pattern caused by the light beam “bending” around the corners of the slit.

Light diffracting through a slit — Image source

But what happens if you get two of these slits, and put them close enough together? Then the waves start interfering. Because of the way these waves are oriented, you get parts of the new wave that interfere constructively, giving you twice the brightness, and parts that interfere destructively, giving complete darkness, and you end up with a nice little pattern of bands. All this makes sense if you think of light as a wave.

The double-slit experiment — Image source

Let’s step aside for a moment and talk a bit about what happens to a light wave as it reflects off a mirror. Roughly speaking, whenever light is reflected off a mirror at a right angle, it gets its phase changed by 90°. In other words, look at the red line in the graph below — notice the wave’s repeating pattern? It gets shifted backwards by about one quarter of the length of that repeating pattern, forming the blue line.

The red line is shifted backwards by a quarter of its wavelength, forming the blue line — Alternate version here

This lets us do some cool things with mirrors to study interference. There’s one type of mirror that’s pretty useful for these kinds of experiments, and that’s the half-silvered mirror — a neat little mirror that reflects only half the light shone onto it, and lets the other half pass through.

Take a look at this experiment here:

The half-silvered mirror experiment — Image source

In this configuration, A and D are half-silvered mirrors, while B and C are normal ones. Mirror A splits the beam of light into two, and at mirror D each of the two beams is split again, and goes into both detectors. If you study this closely, you’ll find that there are four paths the light can go through: ABDE, ABDF, ACDE, and ACDF. Furthermore, at the end of the experiment, beams ABDE and ACDE end up joining together and going to the same place, as do beams ABDF and ACDF. Let’s look at these two pairs.

Both ABDF and ACDF are reflected exactly twice, which means they get phase shifted by 90°+90° = 180°. But since they both get shifted by the same amount, they stay “in-sync” (in phase), and therefore interfere constructively.

ABDE and ACDE are a different matter. ABDE gets reflected three times (a 270° shift), while ABDE only gets reflected once (a 90° shift). This means that the difference in their phases ends up being 270° – 90° = 180°, meaning they are completely “out of sync” (out of phase), and interfere destructively.

What this all ends up boiling down to is that you get all of the light flowing towards F, and none of it flowing towards E. And again, this all makes perfect sense when you think of light as a wave.

Light as a particle

As it turns out, though, light has some behaviour that is inconsistent with the idea of it as a continuous wave like ripples in a pond. (Fun side-note: before the discoveries that led to the concepts of the photon and relativity, this is exactly what scientists thought light was — some kind of ripple in a mysterious “aether”.) It was discovered that light gave its energy in fixed amounts — its amounts being equivalent to the light’s frequency (how fast the wave is waving) multiplied by a number now known as Planck’s constant (usually denoted as h, and whose value is 6.62×10⁻³⁴ Js).

This is a rather baffling result if you consider light a wave — it’s like having a pond in your backyard where the ripples can be 1 cm high or 2 cm high, but can’t be any other height in between. So the concept of the photon came about, that light was a series of point-like particles flying around in space. Further experiments supported this model.

(Fun fact #2: This is where the term quantum comes from — the energy in photons and other particles is said to be quantized)

Where it all breaks down

All this presented a problem, though, because now, somehow, the two seemingly very different models of light had to somehow be reconciled. And it gets weirder from there.

Remember those interference experiments we talked about earlier? Turns out the interference still happens even if only one photon is sent through at a time. Consider the double-slit experiment. Those bright areas that you saw? As it turns out, a photon is more likelyto end up hitting one of those areas than the darker areas. You can see that pretty clearly in the image below (though this was done with electrons, the concept is the same) — each dot is where a particle hit, and you can clearly see the bands of high probability.

An animation of the double-slit experiment done one particle at a time — Original image source

The same thing happens with the half-silvered mirror experiment — even if you send one photon at a time, they will always go to only the one detector with 100% probability, never the other.

So, it looks we’re dealing with a wave of probability, then, as strange as that sounds. But it gets stranger.

Let’s take the half-silvered mirror experiment again, but let’s put a sensor in one of the beams that detects the light going by without blocking it, to see if we can tell which path the photon takes.

The half-silvered mirror experiment, with a sensor in it this time — Image source

What happens? The interference completely vanishes, and you get an equal chance of the photon going to either detector again. The same thing happens if you try and put a sensor on one of the slits of the double-slit experiment, to see which slit it passes through — poof, interference gone. And everyone is thoroughly baffled.

This is where you have to really plunge into the quantum world to understand it.

Superposition

The best way to think about these things, really, is not to think of them as ripples in a pond nor billiard balls flying around in space, but instead as a flow of probability. In the half-silvered mirror experiment (without the sensor), don’t think of it as “the photon has a 50% chance of being reflected or not reflected”. Instead, realize that the photon takes both paths. 50% of the probability flow is reflected and takes the upper path, while 50% of it is transmitted and follows the lower one. This is what we call a superposition of states — one state is the photon being reflected, the other is it being transmitted through the mirror, and the photon exists in a superposition of these two states, that is, both simultaneously. When these flows join at mirror D, again they take both the path where they’re reflected and the path where they’re transmitted, and because these probability flows are waves that obey the same principles we talked about earlier, the probability flow going into E gets destructively interfered (meaning 0% probability) while the probability flow going into detector F gets constructively interfered (meaning 100% probability).

The same happens in the double-slit experiment — the photon takes every path through the two slits, and the probability waveform interferes with itself to give us that cool band effect.

(A note to any scientists reading this: I’m trying to avoid the whole “squared-modulus” thing here because I’m trying to avoid math as much as possible. To those who are interested, you can refer to other sources. To everyone else, suffice it to say that the math for figuring out the probabilities is slightly more complex than I’m laying it out here.)

Scientific Divisions

This still doesn’t really explain why we only see the photon in one place, though, rather than spread out. And unfortunately, this is where modern-day scientists are divided. In general, it seems that whenever we observe or measure a photon, it causes that probability waveform to “collapse” and the photon to show up in only one place. There are two major interpretations of this: one is the Copenhagen Interpretation, and the other is the Many-Worlds Interpretation.

As an important side-note here, though you may have figured it out earlier, these quantum effects don’t just apply to photons — all particles experience these effects, though the bigger they are, the harder it is to see them. (Though interference has already been shown even in large molecules like Buckyballs). In any case, I’m now going to stop talking specifically about photons and start talking about particles in general.

In all honesty, I personally don’t prefer the Copenhagen Interpretation. It’s never made much sense to me. But I’m going to try and explain it as best as I can. The idea behind it is more-or-less what I said in the first paragraph of this section — whenever we try to observe a probability waveform, the wave “collapses”, getting rid of every point of probability except the one where we actually end up seeing the particle. So when you put a detector on your double-slit, it ends up collapsing the photon before its probability wave can create the interference pattern, and the pattern vanishes.

For practical purposes, this works, but I’ve always found it a bit odd, because it never explains why the waveform collapses like this. This is why I prefer the Many-Worlds Interpretation, which I’m going to get into soon. But first, I need to introduce some more concepts.

Decoherence

Let’s consider a particle that’s travelling along in space, and another that’s stationary. Let’s call the travelling one P1 and the stationary one P2. Let’s say that P1 is in a superposition of two states that are in two different positions, one that will collide with P2 (blue), and another that will miss it entirely (red).

What do you think will happen when P1 reaches P2′s position? Obviously, if it were entirely on the left, they would collide and both go off in different directions, while if it were entirely on the right, P1 would miss P2 completely and continue travelling while P2 stayed in the same place.

But P1 is doing both those things. Both the collision and the non-collision will occur, and you’ll end up with P2 both being collided with and not collided with, flying off and staying perfectly still.

And these two superimposed states are vastly different, meaning that the “blue” state of our little two-particle system is now even more significantly different its “red” state. You can intuit, then, that seeing any sort of interference between P1′s “blue” and “red” states would be much more difficult after it collides with P2. This is a rough explanation of decoherence, where quantum particles have less and less interference as they interact with other particles.

The Real Mind-Blowing Stuff

Okay, so we’ve covered decoherence, but how does this help us understand why we only see the photons in our double-slit experiment in one place? Well, consider this: the screen we’re projecting our photons on to in the experiment, what is it made of?

Atoms. Quantum particles/probability waves.

It makes sense, then, that as the photons pelt the screen, that the atoms in the screen would decohere in the same way that P2 was decohered after P1 (half-)smacked into it. Let me repeat that for emphasis: the whole screen is decohered, is brought into a superposition of states, every time a photon pelts it.

And your eyes that are looking at that screen, receiving photons that are reflecting off it, what are they made of?

The same thing — atoms, particles.

As the photon, superimposed into a billion different states, each of them travelling in a slightly different trajectory, hits the screen, so too does the screen decohere into billions of different states, each one where the photon hit in a slightly different position. And as you stare at that screen, the light bouncing off the screen also decoheres your eyes into a billion different states.

And what about your brain? What is it made of?

As your eyes are decohered into a billion different states, so too are the signals that your eyes send to your brain decohered into a billion different states. And then, as those signals reach your brain, so too is it decohered.

And somewhere within the mess of all these superpositions, one of the superimposed states of you says to your lab assistant, “The photon hit the left side of the screen,” while simultaneously another one of the superimposed states of you says “The photon hit the right side of the screen”. And both of these would be equally real, as real as what you’re experiencing right now.

That, my friends, is the Many-Worlds interpretation of quantum physics — that your body, brain, and everything around you is constantly being decohered into a superposition of very different states by every single photon, every single particle, that interacts with it.

And that is the most mind-blowing thing I know of in physics.

Source: XKCD

It’s far too often that when confronted with that quiz I have to study for, or that problem set that needs solving, or that assignment that I really shouldn’t be leaving to the last minute, I’ll instead take a “short break”, come across some new and interesting webcomic, and find myself hooked, clicking through its many-year-long archive one page at a time.

But this isn’t a story about procrastination. That’s just the backdrop. The story I want to tell is one of an interesting contrast, of “magic”, and of talent.

A while back, when procrastinating from doing something-or-other important, I found myself flipping through the pages of Girl Genius. 

Source: Girl Genius, Vol. 5, p. 38

The comic is an entertaining one, set in an steampunk-styled alternate universe where brass-colored gear-filled robots are common, airships are the most efficient method of transportation, and folk stories of technological adventurers abound. It tells the story of Agatha, who is a talented inventor, sole heir of the Heterodyne family, and powerful Spark.

Wait, powerful what?

That’s right, a Spark. You see, in this universe, only a small selection of people are able to build complex machines and robots. These people have a power — the “Spark” — that gives them this ability, allowing them to enter a state of extreme focus. They are also frequently insane. But this ability leads them to be some of the most powerful people in the world.

Source: Girl Genius, Vol. 7, p. 44

As an engineering student, this amused me to no end. It seemed to me that this was a warped view of engineering through an artist’s eyes. They see the work of engineers and other technical people, and are amazed at the talent they’re showing and their skill with machinery and technology. Why, it’s practically magical! What they don’t see is the years of study, experience, and practise that it takes to get to that point. They don’t see the pages of notes and practise problems when trying to understand introductory calculus. They don’t see us beating our heads against the desk trying to fix the compiler errors in our first Hello World program. They don’t see us baffled when our calculations show that the elevator would need negative three steel cables to keep it from falling. They see the result of all that, and when you just look at the end result, it really does start to look like magic.

On a separate bout of procrastination, I found myself clicking through the archives of Questionable Content.

Source: Questionable Content #1943

Questionable Content is set in a considerably more mundane world than Girl Genius. It’s about a group of twentysomething indie rock fans, who do silly things like date each other and get into shenanigans. Oh, and there are also sentient talking robots, but they’re incidental to the story, really.

But this time, the content of the comic isn’t what’s important. You see, Questionable Content has been around since 2003, and has always kept a regular schedule. That’s nearly ten years of content, updated 2 or 3 times a week. Girl Genius has been around longer (though it’s only been on the web since 2005), but there’s a significant difference: Phil and Kaja Foglio, the main duo behind Girl Genius, were professional artists and writers before they started on Girl Genius. Jeph Jaques, the man behind Questionable Content, was not. His job was answering phones for a local newspaper. Going through the comic’s archives you can see his progression as an artist, all the way from the beginning.

Marten Reed looking awkward throughout the ages.

It’s not a sudden jump in skill, either. While reading through the archives, the improvement was so gradual that I barely noticed it. At some point I realized, “Hang on, when did the characters stop having pencil-necks?” I jumped several hundred comics back, and only then did the magnitude of the improvement become apparent.

And that’s when it hit me. Engineers think of artists in the same way that the artists of Girl Genius (presumably) think of engineers. We say people have a “talent” for art, but ignore the years of consistent practise that is required to get to that point. The archives of Questionable Content throw this fact into sharp relief, because you’re flipping through years of work over just a few hours, putting the slow improvement of Jeph’s skills into fast-forward. But other artists? You’d have a hard time finding material from the beginning of their career (and they might even be too embarrassed to show you).

Next time you see someone talented, whether it be in math, art, music, programming, or anything else, instead of saying to yourself, “I wish I was that talented,” consider the patience and dedication it took to get to that level. If you truly do want to be that talented, perhaps it would be worthwhile to pick up a pencil, start writing some code, or sit down with your instrument.

And that’s the story of how I learned a valuable lesson about effort while slacking off from my work.

I don’t own a good camera, (or even a decent one) but it was very beautiful, and so I couldn’t resist snapping a few shots with the crappy camera in my iPod Touch. Others there were better prepared, and the place was lousy with photographers, as well as couples and families who wanted to take in the sights.

The crowds were there for good reason, too. The cherry blossoms, or sakura as they’re called in their native Japan, only flower for about a week, after which the delicate petals fall to the ground to make way for the leaves.

Because of their ephemeral beauty, the cherry blossoms have gained a reputation as a symbol of transience. And that got me thinking.

Let’s take a look back to my childhood. When I was a kid, my family and I would take occasional trips to High Park, whether it was to go see the zoo, to swim in the pool, or to let my brother and me play in the playground. But when I was about eight or nine, a man named Jamie Bell did something amazing with the help of some enthusiastic members of the community — they turned their ordinary playground into an enchanted castle.

The pictures you see here are from when I was nostalgically wandering around the playground in the dead of winter a few years ago. The camera I had then was even worse than the one I have now, so please excuse the picture quality.

And what a castle it was. Your ordinary playground would have some slides, swings, maybe a jungle gym — this had all that and more. It had multiple floors to the castle with labyrinthine corridors, swings, musical toys, several slides, and more. This was more than just a playground — it was a kingdom, built for children like me.

The biggest slide in the playground.

It even had its secrets. Down in the “dungeon”, there was a tiny opening, just big enough to squeeze through, that led to the area behind the big spiral tube slide. This part of the structure was walled off and inaccessible from the outside, presumably so kids wouldn’t be able to climb up the outside of the slide. But if you knew about this secret entrance, the world was your oyster. You could climb up the slide, you could bang on it to spook the kids sliding down inside it, or you could just go and hide there, away from the rest of the playground.

In the “dungeon”. The secret entrance is the hole on the left side of the image.

In retrospect, that entrance was probably meant for maintenance access, but it held a certain mystique to me as a kid. It was somewhere where you weren’t “supposed” to go, somewhere that the adults couldn’t find you. My own little hideout.

But about a month ago, someone lit the playground on fire.

I was on my laptop in the living room, the TV idly left on a news station, when I saw the report. It’s hard to describe the feeling that you get when you look up and are greeted with your childhood going up in flames.

After taking in the beauty of the cherry blossoms, and with the thoughts of transience still hanging in my mind, I decided it was time to visit what was left of the playground.

The damage wasn’t quite as bad as I expected. A good part of the playground had still survived, and there were plenty of kids playing there. But the big tube slide, the secret hideout, and the tallest towers of the castle had all been torn down. The good news is that there’s already a strong community effort to rebuild it, but I don’t think it’ll ever be quite the same.

I leave you with an old Jewish proverb I’d heard long ago:

Of all King Solomon’s servants, the bravest and most faithful was Benaiah, the captain of the guard. One day, Solomon called Benaiah in to see him. Solomon intended to give Benaiah a task that would humble him.

“Benaiah,” he said, “there is a certain ring I wish to wear for Sukkot. It is no ordinary ring — with just a glance, it has the power to make a happy man sad, and a sad man happy.”

“If it exists anywhere on Earth, Your Majesty, I will find it and bring it to you,” replied Benaiah, and he was off.

Benaiah searched for months with no success, until, on the night before Sukkot, he decided to go for a walk in one of the poorest areas of Jerusalem. Exasperated with his fruitless search, he asked an old merchant whether he knew of this magical ring.

“Indeed I do,” replied the merchant, and he pulled out a box from his satchel. Inside the box was simple gold band with an engraving on it. It lacked any hint of magic, but the moment Benaiah laid eyes on it, he knew this was the ring he was looking for. He thanked the merchant, paid him his due, and returned to Solomon.

That night the city welcomed Sukkot with great festivities. With a teasing smile, Solomon greeted Benaiah, “My loyal servant! Have you found the ring I asked of you?”

“I have, Your Majesty,” he said, and handed the ring to Solomon.

The moment Solomon laid his eyes on the ring, the smile fell from his face, for engraved on the ring were the words:

This too shall pass

By the end of the last article, we had a physics system in which we could change the following aspects:

• The base acceleration, which, when increased, caused the enemy to move and accelerate faster,
• The angle at which the enemy is accelerating, and
• The coefficient of friction which determines how long it takes for the enemy to come to a stop, and also factors in to the enemy’s top speed.

In order to keep all the enemies moving with a similar “feel”, I kept the coefficient of friction identical for every enemy, as well as the player. If I wanted to, for example, have some enemies look like they’re gliding on ice, while others start and stop instantly, I could change this.

The base acceleration differs from enemy to enemy, but is kept constant for all enemies of that type, at all times. This also means the enemies never come to a stop.

Thus, the only thing that is changed dynamically by the AI is the angle at which the enemies accelerate. This is the parameter that all the AI logic goes into — it only changes where the enemy is supposed to go. This is decided using a couple of very simple rules, but the way this is decided is different from enemy to enemy, and results in very different behaviour.

Let’s take a look at the different types of enemies we have. Lucky Shot only has three types of enemies. They’re never given official names in-game, but I like to call them drifters, dodgers, and shooters.

• Drifters are the simplest and easiest enemy. All they do is chase you. That’s it.
• Dodgers chase you as well, but the moment you start shooting at them they scurry away from your bullets.
• Shooters are different in that they can shoot back. To take advantage of this, they keep their distance from you, circling you at a safe distance — not too far, not too close.

Let’s look at each of these in turn.

Drifter

Click above to play! Use the WASD or arrow keys to move, and click to fire.
Both you and the enemies are invincible.

The drifter is the simplest of the enemies. Their acceleration is always kept in the direction of the player. That’s the extent of their behaviour.

Well, almost. There’s a slight problem with that: if all of the enemies simply kept their acceleration pointed exactly towards the player at all times, as the player dodged and weaved around them, their paths would end up converging, and you’d get all the drifters overlapping in one big clump. To prevent this problem, I add a bit of noise to their motion — instead of accelerating directly at the player, they accelerate in the player’s direction, plus or minus up to 90°. That may seem like a lot, but remember that we’re dealing with acceleration rather than velocity. On average, they’re accelerating towards the player, and that means that their velocity is always going to be roughly towards the player as well. The overall effect of this is that the drifter takes a slightly wobbly path towards the player, and when you have several of them on screen, each of them heads in a slightly different path, keeping them from overlapping too much. This strategy is employed to varying degrees in all of the later enemies.

Dodger

Click above to play! Use the WASD or arrow keys to move, and click to fire.
Both you and the enemies are invincible.

If you’re not firing at it, the dodger acts identically to the drifter, with a few minor differences. It has a slightly higher base acceleration than the drifter, and a slightly smaller range of movement noise — it points itself in the player’s direction, plus or minus up to 65°. This means it’s both faster and travels in more of a straight line than the drifter.

The big difference, of course, comes when you fire at it — it flees from bullets, hence the name. This is probably the most complex of the AI behaviours, and it’s a bit rough around the edges — you may notice that they get confused if there’s a lot of bullets around them on all sides, and they sometimes travel into the stream of bullets rather than away from it. But for the purposes of the game, it works well enough.

First off, they’re not actually dodging the entire stream of bullets. They’re dodging only one bullet, the one that’s closest to them. Each frame, they look for the closest bullet to them, check the distance between themselves and the closest bullet, and depending on how close it is, they move themselves away. If the nearest bullet is all the way across the screen from them, they head towards the player as usual. As the bullet gets closer and closer, they turn further and further away from the player, until, if the bullet is right on them, they head 90° to the player, away from the bullet. By comparing the angle between them and the player, and the angle between them and the bullet, they can decide whether to dodge in a clockwise or counter-clockwise direction.

How the dodger decides which way to run from bullets

How far they turn away from the player is determined by the following formula:

Where is the angle the dodger will turn away from the player  (ex. 0° is directly towards the player), is the distance from the dodger to the closest bullet, and is the width of the stage. If you plug in some values, you can see that when the dodger is a stage-width away from the player, it heads straight towards the player, and when the bullet is very close, the dodger will move at close to 90° away from the player.

This works out decently well in practise, even though there are some cases where the behaviour is a little wonky.

Shooter

Click above to play! Use the WASD or arrow keys to move, and click to fire.
Both you and the enemies are invincible.

These guys are the biggest threat in the game. With the ability to shoot at you, they can cause a lot more damage than any of the other enemies. In doing so, they like to keep their distance, making it harder for you to shoot back, especially if you have a short-range gun. They have a slightly higher base acceleration than the dodger, and only have a 60° range of noise added to their acceleration direction (±30° as compared to the dodgers’ ±65° and the drifters’ ±90°).

The key difference in their AI, of course, is that they keep their distance from the player at all times. To do this, I chose to use a simpler system than the dodgers’ AI, similar in nature but less complex. Depending on the distance between them and the player, they change the direction in which they’re accelerating. If they’re far from the player, they accelerate directly towards the player. A bit closer, and they accelerate at 45° to the player’s direction. At a neutral distance, they orbit the player, accelerating at 90° to the player’s direction. Any closer than that, and they move away, first at a 45° angle, and at a very close distance, directly away. Each of these is hard-coded into the shooters’ behaviour.

The shooters' behaviour is all hard-coded, based on the distance between itself and the player.

This works quite well, and has the advantage of being a lot simpler than the dodgers’ movement system. The simplicity also means that it’s easier to tweak — if I wanted them to orbit the player at a closer distance, or have a wider range of distances at which it would be happy to orbit, it’s as simple as changing a few constants. And because we only change the acceleration rather than velocity, you don’t see an abrupt change in direction when they hit the boundaries.

There’s one thing left in their movement AI, and that’s deciding which direction they’ll be orbiting the player. To do this, I had three options — have them orbit clockwise, have them orbit counterclockwise, or have them choose between the two randomly when they’re spawned. I chose all three options. I had those three options coded in, and chose between them based on what fit the level best. Even in the above flash demo, if you refresh a couple of times, you’ll notice that one of them is always orbiting clockwise, one always counterclockwise, and the last chooses one or the other randomly.

The very last thing handled by the AI is the direction in which they’ll be shooting. This is simple — their guns are pointed directly at the player, but have a spread of ±15°. Because enemies with perfect aim are cheap and boring.

The Final Word

What I wanted to show here is that you don’t have to have a fancy, strategizing, A* pathfinding, neural network creating AI to create fun behaviours for your game. Especially in a time-limited competition like GMD, simple AI is often best. But if you fake it well enough, your enemies can seem appropriately intelligent while still keeping that simplicity of implementation.

As always, I encourage you to email me or post a comment below if you have questions or comments. Happy coding!

Before I get started, though, I’d just like to say that this likely won’t be anything new to anyone who’s programmed a physics system in a game before — in fact, if you have, you will likely see this as overly basic. And it is. This is meant more as a beginner’s introduction and as a showcase on how some very simple ideas can lead to some very nice behaviour. It does, however, require some knowledge of high-school level math and physics.

The development of Lucky Shot started well before the competition even started — the fundamentals of its physics and movement had been developed earlier, while I was playing around with top-down-shooter-style movement and learning Actionscript 3. I came up with the movement system when I was playing around with creating a top-down shooter-style game based on the Doppler effect. The mechanic itself turned out not to be that fun, so I never continued with it, but the simple ideas behind its movement system has powered nearly every game I’ve made to date.

In order to best understand how it works, I’m going to lead you through the same thought and discovery process that I went through when coming up with this. In the beginning, I had just started playing around with Actionscript 3, so I started out by moving a circle around the screen in what is probably the most basic way possible: every frame, the game would check whether the arrow or WASD keys were held down, and if so, it would add or subtract a constant value from the circle’s x and y position as needed. (I called this constant value the circle’s base speed.) This gave me something like this:

 
Click above and use the WASD or arrow keys to move around!

This is a start, and for a simple game this might even be good enough. But there are some obvious problems with it:

1. You move at a constant speed.
2. You stop moving as soon as you let go of the key.
3. Moving diagonally is faster than moving purely horizontally or vertically.

Points 1 and 2 can be summarized in two words: no inertia. So let’s try a different approach: instead of adding a constant amount to the player’s position every frame, let’s try adding a constant amount to the player’s velocity, with a cap on the velocity to ensure the player doesn’t rocket off at ridiculous speeds. This means that the arrow keys would control the direction the player accelerated rather than the direction the player went. This strategy gave me this:

 
Click above and use the WASD or arrow keys to move around!

You’ll notice also that I added a bit of functionality to bounce the player off the walls. This is as simple as inverting the player’s x or y speed once the player is out of bounds.

This is much better already. Now when we press a direction, we’ll accelerate in that direction, and it feels much more smooth. But there are still some problems with this:

1. When you let go of the keys, you never slow down — you’ll keep moving and bouncing forever.
2. You accelerate faster diagonally than you do purely horizontally and vertically.

Let’s look at the first problem. Again this can be summarized in two words: no friction. Let’s add some simple friction.

The version of friction I implemented was inspired by the concept of terminal velocity. When an object is falling in air, that air applies a frictional force to it in the opposite direction of movement. This frictional force is proportional to the object’s velocity, so as the object falls, it gets faster, causing the friction to increase, which in turn causes it to accelerate at a slower rate. Eventually you reach a point where the air friction balances out the force of gravity, and the object’s speed stops increasing.

In my implementation of this, we don’t deal with forces, nor with gravity. Instead of dealing with forces, we can deal with accelerations instead. And instead of gravity, we have an acceleration imparted by keys that the player is pressing, or in the computer-controlled enemies, the AI’s logic.

The first thing we do is figure out the acceleration for the object, which is a constant value (which I call the base acceleration), but may be in a variety of different directions (more on that below). Then, we calculate deceleration due to friction , which is the object’s velocity multiplied by a friction coefficient , which is a number in the range of about 0.05 – 0.1, depending on how much friction you want to give the object.

The deceleration due to friction is then subtracted from the object’s acceleration, and that acceleration is added to the object’s speed. The second-last thing we do is compare the object’s speed to a very small value — about 0.01 — and set it to 0 if it’s below that. This is needed because with this implementation of friction, the object’s velocity never actually reaches 0, it just gets very very close to it. This causes a bit of “drift” when the object slows to a halt, where it keeps moving by a fraction of a pixel each frame.

The last thing we do, of course, is add that speed to the object’s position.

We can tweak the motion of the object by changing the constant base acceleration and the friction coefficient . The bigger we make , the faster the object will accelerate. The bigger we make , the slower the object will move, and the faster it will come to a halt. The object’s maximum or terminal velocity is the point at which these two balance out: . If you want the object to feel like it’s sliding on ice, you can decrease both and . If you want the object to stop and start instantly (similar to the movement in the first flash demo), you can increase both and . And as long as you keep the ratio between the two the same, the object will always move at the same speed.

So now we have friction. You no longer bounce infinitely off the walls, and turning is made a lot easier. There’s just one last issue to address, and that’s the increased acceleration when going on a diagonal. To fix this, we need a tiny bit of trigonometry.

Say you want your little dude to go at an arbitrary angle , but you want to keep his base acceleration as . That is, no matter which direction he’s going, his total acceleration should always be . To use this in the code, we need to break this down to its x and y components, which I’ll call and . This is as simple as doing this:

Plug in whatever angle you want for , use these as the acceleration values for your x and your y, and you have yourself some smooth movement whose speed and acceleration is independent of the direction you’re moving. In fact, if you’re just handling keyboard control — where you have at most 8 directions in which you can move — you can just handle the straight up/down case by just using the base acceleration , and  the diagonals by adding to the x and y values with the sign dictated by the direction (this is the same as ).

Now that we have all this set up, let’s see it in action.

 
Click above and use the WASD or arrow keys to move around!

Wonderful. We now have a movement system that’s smooth, simple, flexible, and fun in and of itself. But here’s the dirty secret: this takes care of most of the natural-looking movement you see in this game’s AI. In part 2, I’ll show you how this system, along with some very simple rules of movement, created an AI system that was both fun and challenging to players.

Last year was actually the first time the club ran the public showcase. We held it during the Computer Science Student Union‘s game night, and to take full advantage of it, we gave out feedback forms, asking people to rate each game and write a few words about it. I found that the reactions we observed and the feedback we got were even more valuable than the prizes given out. With that in mind, let’s take a look at how people enjoyed the game.

You can tell who the Starcraft players were.

But before we get started, if you haven’t played the game yet, go do that now! This article will make a lot more sense if you’ve played it.

Click here to play! (Opens in a new window)

Back? Ok, let’s get down to business.

What worked

Slim, bottom-up game design

This game was based on a very simple idea: a top-down shooter where you gamble for your guns. The gambling element came from the theme for the competition: Don’t be funky, let’s get lucky. But in development, instead of starting off with art, or music, or the gambling element, I started off with the very basics — movement, control, shooting, etc. Nothing extraneous was added until closer to the end. I built up a quick, simple, but very good and flexible framework for the game itself in the earlier stages of the competition, and later on I took as much time as I could to polish it, give it a good interface, and cram in as much content as possible (which in my case meant coding up a big variety of guns).

This can be risky for some people, as you can end up getting trapped in refining the framework and run out of time to build an actual game around it. But if you manage it right, and put priority on the actual game parts of your game, you end up with something playable very quickly. This is especially good for GMD, because of the need to balance the competition with school work. It’s likely that you’ll end up slammed with assignments or tests near the end of the competition, forcing you to hand in what you have done. If you have a playable game from the early stages, you at least have a chance at doing decently despite it being unfinished.

Arcade-style gameplay

This kept the game simple, accessible, and above all else, fun. It would have been nearly impossible to implement a game of calibre similar to an RPG, for example — it just requires  far too much content to make it enjoyable. Arcade games can be enjoyable even if they’re only one level. And in the end, the environment in which they were shown lent itself far better to arcade-style pick-up-and-play gameplay than anything more complex.

Grabbing people's attention in between games of Counter-Strike.

Slick, simple AI system

This was one of the most complimented parts of the game, and it amazes me, because it was surprisingly simple to make. I won’t go into detail on this just yet, but keep your eye on this site, as I’ll be posting up some articles detailing the AI and physics systems soon.

Smooth difficulty curve with a high peak

The idea to make the later levels insanely difficult was inspired by the game Darkest Before the Dawn, made by my friends Francesco Ciarlandini and Sean Lacy for the previous year’s GMD. In their game, while it starts off relatively slowly, as it goes on it gets more and more difficult until all hell breaks loose near the end. Few people still have beaten that game. What I found, though, was that I kept coming back to it, playing it again and again, until eventually I managed to beat it. Its difficulty made it entertaining despite being relatively slim on content (as all GMD games are). Not only that, but the fact that the game treated me as if I wasn’t entitled to beat it made me even more determined to win. So I modelled Lucky Shot’s difficulty curve in a similar way. Most people should be able to get past the first few levels. Few will get past the last couple. And as of yet, I am the only one who has managed to beat the final level (and even I have only ever done it twice).

(As a side note, if you can provide evidence that you’ve beaten this game to me, I’ll personally acknowledge you on this blog as the first person to beat Lucky Shot other than its creator. Protip: save your Machine Guns for the last two levels.)

Doing it right.

What was interesting to me was comparing it against Francesco and Sean’s game from this year, Gamblon 777. This game was quite fun, managing to just barely beat me out for third place in the public showcase. But it didn’t have the smooth difficulty curve of the previous game. I noticed that many people would sit down at this game to play it, die within ten seconds, and simply get up and leave. It shows that you need that slow start in order to get people hooked in the first place.

Gradual introduction of concepts

Tying in somewhat to the above, it’s not just the difficulty curve that’s gradual — it’s the complexity as well. I had three types of enemies. Each behaved differently from the last, and they had a pretty obvious hierarchy in terms of difficulty. I had to make sure the player wasn’t confused by them at the beginning.

What I chose to do was introduce every enemy in turn, each in their own levels. Level 1 introduces you to the basic Drifter enemy that chases you. Level 2 is a slightly harder Drifter level. Level 3 introduces you to the Dodger. Level 4 is a slightly harder Dodger level, with a few Drifters thrown in at one point as a surprise. Level 5 introduces you to the Shooters. And so on. It’s not until the last few levels that they start mixing together in any significant way, and that’s when the game gets very difficult.

This is the same idea used by games like Portal. You have to deliberately train your players to understand and deal with your gameplay concepts before throwing them into situations where they have to manage several of them at once.

Minimalist art style

I’ll make no bones about it: I am not a good visual artist. This minimalist art style is my way of making something decently visually appealing, functional, and quick to make. And it allowed me more time to work on the game’s foundation.

Creative commons resources

Although I would have loved to have composed and created the music for the game myself, I spent nearly all of my time on the gameplay, making that impossible. I later found myself with an uncomfortably close deadline and no music. I knew I wanted an 8-bit style action-style song to compliment the retro visuals, so I popped open 8bitcollective (where all the songs are licensed under CC BY-NC-SA), found a song I liked, and threw it in there. And it immediately made the game much more fun. I’ve always been amazed at how much influence great music can have on a game.

Not to mention that it’s just so much better than anything I could have come up with myself. Exilefaker, you are a goddamn genius.

What could have been done better

Clearer instructions and between-level interface

This was one thing that surprised me. Several of the feedback forms mentioned a need for “more instructions”. Initially, I was confused. How hard is it to understand a game where you shoot red things? But then I realized that one of the most complex parts of the game — the between-level gun selection screen — had only minimal instructions on how to use it.

Whoops.

Not only that, but people seemed to completely miss things that I had included to make their lives easier. Things like the hints on the bottom-left as to which enemies are coming next, the lives indicator, or even the fact that you could hold down the mouse button to shoot.

To fix this, I could have added, on the first between-level screen, some helpful tips about the interface elements of the screen. A simple bit of text with some arrows pointing to the Gamble and Use buttons, describing each, would go a long way to helping people understand it. Highlighting the hint text and lives count in red would help to make them more apparent. And I guess the people took the words “Click to shoot” from the help screen a bit too literally, so it would have been nice to have made that clearer.

Originality, or lack thereof

I’ll be blunt here — this game was heavily inspired by games like Geometry Wars, even down to the enemy types and movements. As such, it doesn’t really stand out as something new or different, and this is a barrier to grabbing people’s interest. I expect it would be more interesting if I had had the time to add more gun types — after all, you’ve never seen Geometry Wars with mines, homing shots, or a nuke before, have you? Which brings me to my next point…

More content

Which in my case would mostly mean more gun types, though it could mean more enemies and levels as well. When I started conceptualizing this game, I had about a page and a half full of ideas for different gun types. The problem is that I ran out of time to implement them. I feel if I had managed my time better I could have done so.

Getting into a bit more detail, the limiting factor here was not actually the gun types themselves — it was the different types of bullets that I would have had to implement. By the end of the project I had exactly one type of bullet — the standard, round, travel-in-a-straight-line type. It was very easy to create new guns that would fire them in different directions, each with a different speed, range, and damage. It would not have been easy to create guns with bullets that curve, orbit, explode, split, penetrate, swarm, or home in on enemies. Some of those would require a new movement system. Some would require a different collision detection system. Some would even need AI. It just wasn’t feasible to add them given the time frame I found myself in near the end.

But it would have been so damn awesome.

The final word

Although there is definite room for improvement, I doubt I’ll revisit this game anytime soon, with the possible exception of some minor retrofitting to work with the upcoming UTGDDC arcade cabinet. The game is already good as it is now, and I’ve been spending my time recently on other projects. Still, this was a great experience. It was the first time since I got into game development in which I felt I had made something I could be proud of.

But in the end, it’s not my game anymore. It’s yours now. So play it, tell your friends, send me feedback, and most of all, have fun with it.

Click the image to play!

Your questions and feedback are welcome as well. You can post a comment here or send me an email. Also, keep an eye on the blog in the coming weeks: a postmortem will be coming soon, as well as a breakdown of the game’s simple physics and AI systems. Hope you’ll enjoy it!