Zhampres

check it out here:

https://play.google.com/store/apps/details?id=com.austinweaver.chness

The chaos game, on its own, is relatively simple. It yields interesting pictures like these ones:

The algorithm by which these sets of points are created is very simple:

First, choose a set of “focus points”. Let’s call these points A. For the best images, choose between 3 and 7 points. The convex hull of A will be the convex hull of the generated fractal.

Next, choose a random point, we’ll call that point “p”. This point will be the lone element of a set of points called P.

To iterate the fractal, for each point initially belonging to P, add another point halfway between that point and a random point in A.

Iterating this way will lead to the number of points in P doubling each iteration. In the case of my images, I generally went about 22-23 iterations deep, yielding a set P containing about 8 000 000 points.

So as the usual logic goes with these types of images, how can we make this cooler?

Well, an observation that can be made about these images, and in fact all images created by the algorithm described above, is that they will never contain curves. The nature of the algorithm is that it will only produce images composed of straight lines.

To fix this, there is a simple and elegant thing that can be done to the algorithm: simply add some nonlinear transformation between each iteration.

Many nonlinear transformations lead to interesting effects here but perhaps the best I found is what I call the “square to circle” transformation. Rather than describe the transformation here, I will simply link to a desmos calculator that will do a better job explaining than I can:

https://www.desmos.com/calculator/cnj5lbybri

This simple addition to the algorithm yields far better results:

These images are far better to look at.

Now the only thing to add is animation. The images will be animated by rotating the focus points around the origin on the unit circle. The gifs use 3 and 4 focus points respectively.

So the other day I wrote a word and poem generator. It works pretty well: all the words are phonetically correct, although hard to say still because of the foreignness. Here are some samples of what it generates:

1-Syllable Words:

ops frersh ronth warls ens um prend wums wu flask jeng shrar orsh ars clast perls sno greds

2-Syllable Words:

yigrir trognir pletwe afrars zushruf feshet ugri hiblinch grudorch plashrul zeprersh glafem strugnugs ogluds nuscriss

3-Syllable Words

flegglepi treniplod vatwufix dristrafflass smanitesp asmeghot sclocluscli wachoghant iteclox splithwathels anosplanth plegloyent shwusplewost wawigni gifrushund

10-Syllable Words

stroclafrebblucrucrulashrustuyu slibruchostrusprewuscratwugloshweds swuffliteshritwosplosplotiblusneff iswisebblosclopplefoscrustufuck isprabrishwaslabewushrashredrezz plopplescromufluwegglabblablathin

Haikus

obril gleplosp thwop othrig flurch graplu snerls thwesh tregarls slashwups esk

Limmericks

egglong dril rint crab gne rochup quishrug frigni brushed sclesk shrup amecks depraf grils sist stubuns smi ils thiglo setrund izz zutems twup

The actual options for things to generate are poems (given rhyme scheme and syllable counts per line) or words (given length).

So it becomes apparent that the words have a specific feeling to them, as though they’re part of an actual language. This is due to the way the words are generated: I use four lists of letter sets to create them: one for each of beginning, middle and end consonants and one for vowels. These lists can be easily altered and will change the “flavor” of the words generated.

Explanation and Some Extras:

The basic idea is that these are created from simulations of a desk toy called a magnetic decision maker that happens to exhibit chaotic behavior. This is what the toy looks like:

The way it works is: a magnetic ball is at the end of a rigid wire and is allowed to pivot freely on its sphere of possible positions. Gravity pulls the ball down while magnets hidden under the answers attract the magnetic ball. The magnets are strong enough that the ball will never settle in the middle but rather will “choose” one of the answers, giving a seemingly random answer thanks to previously mentioned chaotic behavior. For rendering simplicity, the system will be rendered as viewed from directly above. Here’s a gif of the simple simulation. For simplicity and clarity, the ball is rendered as a white circle and the answers (attractors) are replaced with red circles. The ball’s path is traced by a white line.

So that alone is some pretty cool behavior. We could start the point anywhere, but the point with the wire parallel to the ground just gets the most interesting path. I wonder if we could somehow show where each initial condition would end up, in one convenient image... We can! Simply using color to indicate position is the easiest way to do this, as it allows us to indicate at each point, a different position. Let’s start by making a “legend”, assigning each point in the set of possibilities a color. The easiest way to do this is to use a hue wheel. If we color each point based on its own assigned color, we get this image:

It would be normal hue wheel, but I’m lazy with my programming and real hue cycles are a pain. In this specific case, we’re only interested in seeing which attractor the ball ends up pointing to. This means as long as the colors in the white circles (which attracted points will have) are distinct enough, we should get the information we’re looking for. So what happens if we let the system evolve, and color each point based on where a ball starting there would be at each time? The answer is some cool psychedelic gifs:

The bad quality is thanks to the astronomical size of gif images that have continuous rgb colors and the length of this one. Also tumblr’s gif upload size limits. Anyway though,

It’s pretty easy to tell what happens: as the system evolves, certain areas all converge to a solid color while the outer points turn into static. This actually makes perfect sense: if you drop the ball right next to the attractor, the ball will simply stay there, giving you an extremely predictable answer. However, if the ball is dropped from closer to the equator of the sphere, it will swing around for a long time before settling on which attractor it chooses, taking a complicated path. The chaos is evident in the random static of colors near the edge of the circle.

This chaos can be seen in the simple simulation as well by tracking two points that start very close to each other: the white ball and path from before will now be rendered as coral and cyan, with the coral and cyan balls slightly offset from each other initially, precisely starting 0.001 units apart when the wire is a single unit in length.

I would love feedback if you read this and have any suggestions or thoughts.