experiments

The chaos game

Throw a point at random through the maps, plot where it lands, and a theorem guarantees the attractor draws itself. The renderer is trivial. The tone map is where the work is.

The derivative is nilpotent, and the shift is its exponential

Differentiate a quintic six times and it is gone. Exponentiate that same dying operator and you get the shift by h, invertible forever. The sentence connecting them is Taylor's theorem.

Products add, composition multiplies

Two ways to combine polynomials, two different laws for the degree. One of them proves in a single line that the only invertible polynomials are the affine ones.

Degree is a coordinate

Substituting ax + b into a polynomial is a linear map with a triangular matrix. The diagonal is the powers of a, which is the whole reason an affine change of variable can never change a degree.

What an affine IFS actually is

A handful of maps that shrink the plane, a theorem that says they have exactly one fixed shape, and a second theorem that tells you how to find the maps for a shape you already want.

What a function does to a space of functions

A polynomial is a point in a vector space. Shifting, scaling, differentiating, and substituting are maps of that space into itself, and the only question worth asking about any of them is what happens to the degree.

Five ways to draw the same fractal

The fractal designer now carries five renderers, an aspect-aware workspace, and a button that hands you a clean PNG. Three of the five were quietly drawing the wrong thing.

New Feature - Download demo image

More crossing lines images.

Varying circle grid and color

Roiling sparks

Experimenting with pixel sizes

Generative Convergence #2 - Ghosts

Generative convergence #1 - Shadows

More one dimensional generative experiments

New Technique - Iterated function system interpolation functions

This is what additivity gets you

All filled in - Animated Generative circles #2

Technique work

Another generative geometric fractal experiment

Ring around

My First canvas experiment

Bouncing Circle Grid

Supercharged performance

Grids of circles

Circled out

Infinite Flow

Bouncing circles

Connected components in cellular automata

More animated Circles

A Random Walk Through Some Cellular Automatons

Cellular automaton #1

Distortion

A minor update - circles

Canvas Line Based Image Renderer

HTML5 Canvas Image Effects

HTML5 color eyedropper

Messing around with the canvas mask api

Random dynamics on a triangular grid

Fractal Drawing Tool - Users Guide

Flitter and flutter

Nothing fancy: Winter bubbles

Forgot to upload this image

Islands of stability

Sensitive dependence on initial conditions

Ensemble #2

Ensemble #1

More envelopes

sine waves and envelopes

WebGL buffer fractal renders

Playing around with straight lines

A little free time

Rough and Random page

Quality of Movement

Something I'm playing around with.

Release often

Atomic Orbitals now a chrome experiment

The best surprises come from unexpected places

Just a quick update

three.js particle system

I'm just playing around with particles for this one

Speed of sound

Now we're getting somewhere

Lorenz attractor v1

Closer to a good stopping point

I think this is the last moving fractal for a while

faster, denser

New streaking and pause

Improvements and effects

Animate2

Now with Movement

chrome fractals