I want to talk about the medusa head, an enemy that has appeared in at least as many games as the goomba in Super Mario, but which moves in a more complex way. The pattern it follows is called a sine wave, and it was inevitable that a memorable entity in one of the most important early video games would be built around it.


The Perfect Moves of an Asshole Video Game Bad Guy

1) The sine wave is about the most complex movement pattern that is still easily predictable. Being faced with an obstacle that moves in a sine wave will therefore be challenging and fair. Challenge and fairness is what creates fun.

2) The sine wave is a function of such enormous mathematical depth and beauty that you could spend a meaningful lifetime studying it.

The key to the future of great game design lies in the realisation that the above two aesthetic features are linked in the strongest sense; they are close to being identical propositions.

To expand on 2), we first think about periodicity. The medusa head traces out a "~" shape with perfect smoothness; they then trace out further ~ shapes with perfect symmetry. That sequence has a specific amount of time it takes before it repeats itself. We call that time its "period", and in playing Castlevania you will get to know that period as well as you know your own heartbeat.

To break the movement of the head down: the horizontal velocity stays the same at every instant, and the vertical velocity changes at every instant. The vertical acceleration also changes at every instant. However, none of these variables will ever experience a sudden change. To understand why that is important, think about how it would feel if the medusa head moved in a sharp zig-zag (i.e. the vertical velocity is a positive constant, then negative, then positive etc). The practical difference would be tiny, but suddenly it's harder to predict and less beautiful.

These features of the medusa head's behaviour are mathematically elegant, deterministic, and slightly complex. And these features are all fun.

Castlevania I

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Medusa heads are seen for the first time on the second level of the original Castlevania.

The very first of them appear immediately after you enter this room from the right, which uniquely means that your avatar must be on the far right of the screen (the camera usually keeps the player in the center). As a result of this, you get the safe opportunity to closely inspect the way the heads move. After an establishment of the movement this clear, the level designers can quickly get creative and combine it with other challenges.

The second medusa head nest is in a room of platforming challenges put together with extraordinary density and variety; it is depicted below. The heads will spawn infinitely, but only while you're inside the green square. The path the player usually takes is indicated in grey. The separate setpieces are numbered in yellow (yes, there are that amount and more of them in this 750×175 pixel room).

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1) A two-block-wide jump – ordinarily the most trivial jump possible, made complex by the heads.

2) The tiniest platform it is reasonable to have, where the player must learn to fend off heads essentially without any ability to move left or right. The player may realise here that if you keep still, you have less to fear from the heads. This will be important later.

3) A jump with a vertical element – a small but demanding change. In a devilishly concise and unpatronising move, the designers stopped static jumping challenges here. These two were all that was deemed necessary to present. In later Castlevanias, we do many more jumps while the heads attack us. Almost all of those jumps are nothing but simiplistic variations of the two that we can master in the corner of this one room.

4) The right edge of the green box is positioned to send a dramatic message. The player can exit the box while standing on this platform – this will allow them to make the next jump without heads around, so they want to do it. But bear in mind that the box is invisible. So the abatement of medusa heads acts as a reward for general prudence: if the player inches toward the end of this platform, they receive the pleasant surprise of calmness; if they hastily run and jump, there will likely be a residual head coming straight at them when they are in the air.

5) The faint brown platforms move left and right, and though they come close to the edge, they will never touch it; the player is always required to jump off the platform. So when this platform takes us left, back into the box, we have another jump to make – and we need to hurry up and do that jump, or we shall be punished.

The player might be timid: they may stay on the moving platform, reluctant to make the jump at their first opportunity – they might wait on the platform, hoping to go through with the jump when they're taken back again. But if they do this, a medusa head will appear! They should have jumped while it was safe, so they could be on firmer footing when this head comes. This event can be extremely frightening: you thought the medusa heads had stopped coming for you a while ago, but now you have to perform a jump that factors in medusa heads AND the movement of the thing you're standing on!

This sends us a message: "while an environment is peaceful, make the most of it". It works together with 4), which said to us: "while an environment is chaotic, be careful and hope for change".

6) Due to the limits of the engine, the camera will stop scrolling to the left when the avatar reaches this exact point – but you still have to leave via the door on the left. When you're here, there will be medusa heads coming from the left. So you have to run straight into them, while giving yourself less and less room to see where new ones are coming from! This is scary – you'll be extremely grateful for the dip just before the door. In every other room with heads, either they will leave you alone at some point before your exit, or you will leave via the ceiling.

I believe that fun comes from each of these situations individually; they all create different possibilities that the player has to use their head to respond to. There is something I've neglected, which is the fact that the designers went to great lengths to put all of these situations in the same area. I don't find this assembly very meaningful, but I could be being stupid here. If you're more interested in the structure of the whole, see this groundbreaking article by anna anthropy, and be sure to check the picture posted in the comments by plvhx.

The original Castlevania has a couple of other medusa head nests, each with a structural twist or another enemy teaming up with them. In another display of dedication to conciseness, each of these twists appears in one and only one room.

The most interesting of these rooms contains an infamously challenging pair of axe-throwing knights. They encourage a strategy which requires you to think in an abstract and analytical way about your problems:

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In coming up with a strategy like this or one of its variations, the medusa head is best thought of as a line, rather than a moving point. You have to picture that lovely sine wave as a rigid presence on the screen. It only works if you keep still, and what a glorious stillness it is. With a few inputs (just attacking and ducking), you can gain control over a chaotic and dangerous situation. This is perfect action game design, a setpiece that can be conquered with caution and knowledge while still being elegant and emotive. It spoke to me: "Do not try and overcome raw complexity; find a way of making things simple for yourself" it said.

Castlevania Bloodlines

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Bloodlines has the three most distinctive medusa head setpieces of the rest of the Castlevania series. It's worth saying that broadly speaking, Bloodlines' level design is similar intent to the original, but it is also built to make use of those most interesting capabilities of its platform, the Megadrive. It has interactive scenery, multi-sprite bosses, optical illusions, and skews and rotations galore.

Going into the first medusa head nest, you're standing on a raft in a flooded tower with water draining out, so there's a forced downward-scroll. Your raft is stable, so the screen and your avatar have a constant velocity. What happens to a sine wave which you look at while moving downward? It becomes a gorgeous sin(x) + x wave.

Note that the candles lead the player down a specific route, and that the smallest gap is at the bottom. That gap takes you right up to the wall. Recall that the most dangerous part of a medusa head nest is anywhere near the sides of the screen.

The second setpiece, in the next level, involves climbing up the Leaning Tower of Pisa, which is rickety and narrow (so: you can't get all the way to the left or right of the screen). The camera is now constantly scrolling upward, so the function is a smooth sin(x) – x. But now there's no raft to carry your avatar; you must travel with jump arcs that crisscross the medusa heads' paths.

Bloodlines' final use of the heads is in a sublime room. I lack the vocabulary to describe or analyse it. Suffice it to point out that it shifts the function in a careful and clever way.

Note that a challenge based on this visual concept, wherein an enemy moves between the two viewports, would not work with anything other than the medusa head. A ground-based enemy has one dimensional movement, so it doesn't move enough. The heads are not the only enemies which can leave the ground, but all the other flying enemies have AI, and so their unpredictable behaviour takes center stage when you fight them. Only the medusa head is sufficiently simple, variable, and clean.

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So we see how versatile the medusa head is. Its balance of complexity and predictability make it a perfect tool that the level designer can use to do fascinating things.

It's upsetting, then, that our story leaves the Castlevania series here. None of its entries other than the original and Bloodlines has had level design that really tries to do anything interesting with the heads (though Dracula's Curse comes close). In modern Castlevanias, enemies have to be fun to grind, and level layout can't be allowed to hinder your cartographical endeavour. As egoraptor tells us, nobody would want to backtrack through something in the style of the axe knights setpiece.

Epilogue

A little while ago, Jon Blow and Marc Ten Bosch gave a lecture called Designing the Universe. They offer an unpatronising and expressive idea about what it means to have well designed gameplay and levels – and the enemy placements we've looked at today are an almost perfect manifestation of those ideas.

The medusa head's design is rich in gameplay possibilities, elegant, and unlike any other enemy.

The medusa head's use in levels is varied in a great many expressive ways. You get to know it extremely well, you are made to think of it creatively.

The first Castlevania was made by a small team; it is natural that we should find its real successors in independent video games.

The gleeful and self-affirming decision to break up the viewports in that room in the final level of Bloodlines was fleshed out in "Where Is My Heart?", one of last year's best games.

We have sine wave experimentation in its rawest (though not best) form in Sincar, and a more thorough exploration seems likely to be provided by Waveform. Remember that when things became maximally demanding in the axe knights setpiece, we found that the head was better thought of as a line than a point. Well, in both of these games, the makers give us a helpful line of projection for the entity travelling along the sine wave. This is a more concrete piece of artistic progress than you are ever likely to find anywhere else.

Hamish Todd is a writer and game designer. You can follow him on twitter @hamishtodd1 and read his work at www.actionbutton.net and www.insertcredit.com. He used VirtualDub and online-image-editor to make the gifs. He uses savestates, within reason.

This post originally appeared on Kotaku Australia.