An interactive descent
The Fractal Abyss
A finite rule exposes an inexhaustible frontier. Choose a region, then descend until familiar geometry loses the pretence of scale.
Resolving the boundary
1×Re −0.55Im 0
01 / THE RULE
Infinity from iteration
For every point c on the plane, begin with zero and repeatedly apply the same small instruction: square the previous result, then add c. If the value escapes towards infinity, the point is coloured according to how long it resisted. If it never escapes, it belongs to the black interior.
The boundary between those fates is not merely complicated. However far we magnify it, new filaments, spirals and distorted echoes appear. The rule is perfectly comprehensible; its consequences are not exhaustible.
zn+1=zn2 + c