This is just a quick little demo using the mask API call. It ended up looking a little nicer than I thought it would, so I figured I’d show it.
Random dynamics on a triangular grid
I’m dipping my feet into random and monte carlo methods and wanted to try it out with a triangular grid after finding a few beautiful images on pinterest. I’m just picking grid elements at random and then swaping the values with an adjacent tile.
Everything random moves things around, random plus not separating matching tiles creates small clusters, picking the direction based on the tile color creates big groups in those directions. Rules based on sums just move things around randomly.
I haven’t found any rules to create large scale clusters yet, or create repetitive structured patterns, but I’m still looking. I’ll try some more ising, or changing value instead of swapping rules and see what I can do with those. I would still think that there should be some kind of local clustering rule though.
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Fractal Drawing Tool – Users Guide
Fractal Designer
I’m trying to put together some instructions and add some context for the tool I’ve been using to create the fractal images on the site. I’ve made some updates to the usability and features, adding the ability to upload an image to imgur. This is only the second rev, and the first of more tools to come.
The Controls
This is just a quick collection of instructions on how to use the HTML5 fractal drawing application I have on this site. First thing first, the tool draws images based on the colored control points on the screen. You can drag them around with your mouse to create different shapes.
For even more control, each control point has a set of sliders that control how it adds to the image. The first slider controls the amount of rotation you get around the control point. The second controls how much the control point shrinks the image while it copies. The third which is the most complicated, controls how much the image is squished into a line.
The best way to get a feel for how the images change is to dig right in and start manipulating the graphics. Please let me know what you think on the comments to this post. Things are pretty bare right now, but I have plans to add other renderers that I’ve demoed with pictures, and color for sure. I’ve kept it to black and white as I’m trying to build my skills with more complicated images.
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Flitter and flutter
This is a combination of two previous demos, Winter Bubbles and gravitational slingshot. I’m not sure I like the behavior around the centers of attraction, but it is the best so far. I do like the pulsing trails and color scheme. I’m really trying to branch out there.
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Nothing fancy: Winter bubbles
My inspiration board on pinterest has been filling up, so I wanted to take a few hours to whip up something quick. I really liked the simplicity of winter trees. I didn’t want to do a direct copy, so this is my riff on the composition.
Winter Bubbles
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Forgot to upload this image
After scanning through my blog after the South by Southwest Interactive festival, I realized that I never uploaded an image for my tribute to Ablaze.js.
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Islands of stability
This time I mapped the pendulum angle and time onto the surface of a cone to create a tunnel effect. For the parameter space I’m looking at, you can really see how the paths will converge for a while and then suddenly diverge wildly.
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Sensitive dependence on initial conditions
This next demo highlights the butterfly effect. These curves show the same pendulum as before, this version has the time axis wrapped around the center of the screen and the exponential of the angle as the radius. All the pendulums start at a very similar initial position and for some driving functions they diverge wildly and others they all stay pretty close.
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Ensemble #2
This is more of what I was thinking of when I started down this route.
These are ensembles of particle paths in a chaotic dynamical system. Not only are these ensemble pictures beautiful, but they highlight some interesting mathematics and physics.
But what I’ve really been after is a better source of semi regular noise. The sinusoidal waves and interpolation between random points have been good, but for really entrancing fluid random motion, I need a chaotic semi-periodic source to feed into the other visualizations.
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Ensemble #1
I’m continuing with the envelope series, this time with an ensemble of states of a damped driven pendulum. One of the “classic” chaotic systems. This one isn’t in a chaotic regime, but striking none the less.
