fractals.jelia.nyc

Infinite detail from simple rules

Zoom into a coastline, a fern, a lightning bolt or the Mandelbrot set and the detail never runs out. Each is built by repeating one small rule over and over, and the repetition is the whole secret. This site is a visual, hands-on guide to how that works, from the first "monsters" mathematicians drew in the 1800s to the glowing images computers paint today.

No maths background needed. It starts with what makes a shape a fractal, builds the famous ones with rules you can edit, dives into the Mandelbrot set with a live explorer, and ends with how fractal images get their colours and how a computer draws them in real time.

How it works
WatchEach chapter opens with a short narrated walkthrough. Press play.
PlayLive instruments: a Mandelbrot explorer you can zoom, a chaos game, an L-system editor, a palette lab that recolours fractals as you drag.
ReadPlain-English sections, with "go deeper" panels for the maths when you want it.
Start here · chapter 01What a fractal is Self-similarity, roughness, and why straight lines are the exception in nature.
The famous one · chapter 08Explore the Mandelbrot set One equation, endless detail. Zoom into seahorse valley yourself.
Color & computer fractals · chapters 15–18Where the colours come from Escape time, smooth colour, palettes and palette cycling, orbit traps, light, and the precision limits of a computer.
Why this site exists · chapter 18Fractals that move to music How JellyDazzle draws twenty fractals live, and the bug that made them flash until the fix in 3.6.1.
Contents

Eighteen chapters, a history and a glossary