Thoughts from a Recreational Physicist
I wanted to make something more linear, but not.
In the mean time, I’ve been playing around with angularjs, plus have been installing laminate floors in my house, and I ran into How to fold a Julia Fractal a few weeks ago.  What a fantastic use of 3d at the top of the page, though it doesn’t scroll well on any of my systems.  It’s inspired me to rethink my approach for building interactive demos, and the UI of this site.  Fun stuff ahead.
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.
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.
I just like this one!
I’ve uploaded my very very super rough fractal canvas image editor. This is what I’ve been putting the galleries together with. It’s super rough, I’ll be improving it in random fits and spurts, and putting some demo posts up as well. Also, someone please please suggest a decent title for this one. I’ve got nothing.
This has come together more quickly than any of the other demos. I wanted to see what I could do with a more abstract particle system driven through the same equations I’ve been using for fractals. The old formulas didn’t have quite enough pizazz, so I moved over to the sylvester library for matrices and bumped it up to 3d, which gave me the twisting, darting and zooming I was looking for.
The cantor set is the simplest IFS fractal out there
What is that, Morse code? That my friends is the cantor set. It is one of the examples of basic topology and one of the objects that highlight many of the non-intuitive aspects of infinities.
The most common construction is to take a line and remove the middle third. Next you remove the middle thirds of the two remaining segments. You keep removing the middles of every segment that is left. If you could continue for ever, you would be left with an infinite “dust” of disconnected points.
We can build one with two simple transforms. Just contract by 2/3rds at two different points and the attractor is a cantor set. The next images are going to be simple tweaks of the cantor set, and the fractal space will grow from there.
Square angle and a triangular angle
This image has the 180 angle adjusted to roughly 60 degrees. It looks very little like the original image now.
even less square
This image has the scale for both transforms adjusted as well as the angle of the 180 rotation adjusted. You can start to see how quickly these images change into something unrecognizable as being related to the original image.
roughly square 2
This is similar to the last one, but the angles are 180 and 90 ish. You can see the similarities with the last update.
roughly square
I’m working on a gui fractal image editor, and I’ve been uploading galleries of images I’ve done with it. In preparation to uploading a usable version of it, I’ll be uploading images every day or so.