Curvature of the Mind

Thoughts from a Recreational Physicist

New streaking and pause

paused fractal

paused fractal

I’ve updated yet again. This time I’ve increased the refresh rate and changed the way that I do the motion blur. Instead of keeping a buffer of past images and redrawing them all for each frame, I’m clearing the screen with an alpha factor. That gives a fading trail. I also added a pause on click feature, so you can see a more detailed image if you pause it. Things are starting to come together, and I’m thinking about adding some UI elements to control rate, pause and resume, also hide an show the map indicators with the ability to drag them around the screen.

I also want to work on the movement algorithm to add some more random and compelling movement, like speeding up/slowing down, changing direction, or pulsing through the same point in different directions for a while before zooming off into a completely new area.

Of course I want to add color back too, and experiment with different ways to color the image based on path through the fractal, location, randomness, etc. I’d also like to add movement through the color palette and algorithm as well.

Pause

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Improvements and effects

swirliesI’ve made some changes to the way I’m drawing to the canvas. Using the imageData api is much faster, even though it’s a lot less user friendly. I’m able to keep a histogram of hits per pixel in the image. However, mapping the histograms to the color palette is now going to be more complicated, but I can fill in about 20 times the number of pixels. I’m putting the histogram into the alpha channel and I’m going to play with using the fill mode to mask off an image. In the mean time I ended up commenting out the page clear code, and I liked the trailers it produced. So here it is.

fractal_swirlies

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Animate2

The continual evolution of the animated fractal page. I’ve worked a simple palette into the images giving a slight scintillating effect. I’m testing out markers to show the center, scale and rotation of the maps. They also include more kinds of movement. In the first version, I only included animating the scale and rotation of the maps which lead to a predictable pattern of movement, so this update includes moving the centers as well.

animate2

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Now with Movement

simple fractal

One of the nice things about these images is that they give me the opportunity to talk about some of the more abstract mathematical concepts in a natural environment. These images are rough and don’t look anything like the functions from algebra and calculus, but the are built out of those same simple functions.

The first thing I’d like to talk about is continuity. These images lack many features that I would consider important for a shape. They don’t have distinct edges, sides or middles. Some are just groups of distinct blobs and others are nebulous clouds which don’t look much like anything at all.

In spite of that each one has a well defined “size” and it is possible to overlay two shapes, subtract one from the other and compute the “size” of the difference. This gives a basic concept of distance between the shapes.

One of the neat things about this distance is that you can show the shape generated by these equations depends continuously on the parameters of the equations, so changing one of the numbers slightly produces a correspondingly small change in the shape. That’s what inspired my next page, a random path through a small image space over time.

The images slowly blend and blur into each other over time without jumps or tears, precisely because of that continuity.

animate

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chrome fractals

This is my first attempt at a chrome experiment to generate fractal art. It uses iterated function systems that I learned from Fractals Everywhere that I picked up in college.  It’s really rough, and a very ugly user interface. It’s nothing more than a text area full of json objects and an eval statement hooked up to a set interval statement and a canvas. If you understand half of what I’ve written, then you might want to give it a try and create your own favorite. post them here as a comment if you like it.

/wp-includes/pages/fractal/fractal.htm

Be warned, it looks best in chrome.

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