Fractals Mind Map

Every fractals visualization on this site on one map. The branches are the main ideas. Each leaf is a page; the grey line under it is the one thing to remember about it. Click a branch to focus on it, click a page to open it.

Recall mode hides the page names. Read the hint, say the name, then click the "?" to check.

1. How the map is organized

Overview of the fractals mind map: Escape-time sets, Random iterated maps, Recursive curves, Measuring fractals. — The map at a glance: 4 branches, 7 pages.

Ask how the picture is made:

Each pixel is tested by repeating a formula? Escape-time sets.
One point jumps around and leaves dots? Random iterated maps: the dots fill the attractor.
A shape is redrawn level by level? Recursive curves.

2. The branches side by side

Branch	Rule	Colour or shape from
Escape-time sets	z → z² + c	steps until \|z\| > 2
Random iterated maps	random affine map each step	where the dots land
Recursive curves	replace each segment	level of recursion

3. Five facts to remember

Once |z| passes 2, the orbit of z → z² + c is sure to escape to infinity.
The Julia set for c is connected exactly when c is in the Mandelbrot set; otherwise it is dust.
The chaos game ends on the same Sierpinski triangle whatever the start point.
The Sierpinski triangle has dimension log 3 / log 2 ≈ 1.585.
Each Koch step multiplies the length by 4/3, so the snowflake has infinite perimeter but finite area.

See all fractals pages in the index, or the other mind maps.