Curvature of the Mind

Thoughts from a Recreational Physicist

Closer to a good stopping point

October 15, 2010 by Andy Brummer Leave a Comment

I’ve finally got the chrome crashing bug and crazy memory usage fixed, so I’ve taken a little bit of time while my 3 week old daughter is sleeping here and there to add some refinements. I’ve added basic shading back in, added a link to the blog and a couple of bookmarking links. I’m going to go take a nap now, so check it out:

fractal getdown

I’ve also submitted this version to canvas demos, it would be nice if it was picked up there since I haven’t heard anything after submitting an earlier version to chrome experiments.

Filed Under: Experiments Tagged With: canvas, chrome, fractal, ifs, iterated function system

I’ve got to hand it to IE 9.0 beta

October 7, 2010 by Andy Brummer Leave a Comment

Or then again, maybe not. IE9 is currently the best browser for viewing these images. Chrome keeps crashing after 2 minutes or so, but IE is rock solid running for hours. However, it totally lost the content for this post. It looks like all the script libraries are going to need some upgrades to handle it.

Filed Under: Uncategorized Tagged With: chrome, fractal, ie9, ifs, Internet explorer

I think this is the last moving fractal for a while

October 7, 2010 by Andy Brummer Leave a Comment

I’ve completely revamped the way I generate motion for the IFS fractals. I think it is much more entertaining. Now I generate new points and linearly interpolate between them with the constraint that the sum of the scaling factors is a fixed constant. Before I just generated a fixed path which ended up with a rather repetitive sequence of images. It didn’t matter what image you were shown, you could pretty much see how it was going to twirl into the future.

With this rev, the destination is more random, so the images themselves seem to ebb and flow in a much more organic fashion. I added a 1.5 second pause at the randomly generated point and those images are rendered with more detail.

I’m disappointed that I haven’t tracked down what is causing chrome to crap out rendering, but I’m hoping it’s a bug in the engine that will get patched or eventually I’ll get it figured out.

Anyway, here is the latest version: http://curvatureofthemind.com/wp-content/uploads/2010/10/fractal-lerp.htm

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

faster, denser

September 19, 2010 by Andy Brummer Leave a Comment

WARNING javascript development geek alert.

I haven’t posted in a while as I’ve been refactoring the javascript. I’ve broken the script down into a jQuery plugin to draw the fractals, and moved the ifs animation portion into another level of code. I’m thinking about releasing the code as a canvas based replacement to those “loading” animated gifs on websites. That way users can see something a little bit more interesting than a spinning circle while something is going on with the server.

On the math side of things, I’ve finally worked out a scheme to produce more evenly distributed paths through the fractals. I’ve two minds about this. On one hand, the outlines of the images are more thoroughly filled out, on the other the image is missing some of the nebulous detail I liked in the previous rendering image. I love this. It means I get to choose how each rendering looks. Right now I can choose between a distribution which is evenly selected per transformation or the area traced out by that map. Either the senate or the house of representatives in political terms. Each choice produces a different set of images and I am free to choose the ones that I like best.

So I’ll be playing with those choices and an infinitude in-between. I’ve also got my eye on creating something that will let my viewers create and share images of their own, as well as get into the nitty gritty details of how these images are generated and all the mathematics that goes into them.

Far from being vacuous beauties, there are a number of advanced mathematical concepts that can be explored through them. Topology, probability, measures, geometry, chaos theory, group theory are just the tip of the iceberg. I’ve plans to delve into group theory and generating one dimensional fractals, though it’s going to be a challenge for me. I’ve been more comfortable with short descriptions of the code that I’ve generated, and now I’ll be focusing on the mathematics behind them; I’ll probably be spending a lot more time on those.

Link to the gratuitous new version of the engine here:

http://curvatureofthemind.com/wp-content/uploads/2010/09/fractal_balance1.htm

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

New streaking and pause

September 13, 2010 by Andy Brummer Leave a Comment

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

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

Improvements and effects

September 10, 2010 by Andy Brummer Leave a Comment

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

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

Animate2

September 9, 2010 by Andy Brummer Leave a Comment

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

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

Now with Movement

September 7, 2010 by Andy Brummer 5 Comments

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

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

Gritty Block Header

September 7, 2010 by Andy Brummer Leave a Comment

I’ve picked one of the simple themes, and played around for a minute or two with one of the designs from the last post to get a header image. Now I’m generating them on the page, and I’m using paint.net on a screen shot. I’ll be looking to streamline generating more images and using them through the site. I like this one because it is almost pure texture, and you would be hard pressed to find the self similarity in the image at all.

Filed Under: Images Tagged With: fractal, ifs, iterated function system

chrome fractals

September 2, 2010 by Andy Brummer Leave a Comment

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.

Filed Under: Experiments Tagged With: canvas, chrome, fractal, ifs, iterated function system

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    • 2 simple
    • atomic
    • IFS fractals: 2 transformations
    • random
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    • Atomic Orbitals
    • The surprises keep comming
    • Voronoi

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