Fractal mathematics · Benoit Mandelbrot · 1980

Mandelbrot
· Julia

The boundary between finite and infinite. Zoom in anywhere along the edge — the same complexity, the same self-similarity, the same universe, repeated forever.

scroll to enter
Zone I — Origin & meaning

Indra's Net — known for three thousand years

In the Atharva Veda, the god Indra stretches an infinite net across the cosmos. At every node of this net hangs a jewel. Every jewel reflects every other jewel — and within each reflection, all other reflections are visible, each containing all others, without end. This is Indra's Net: infinite recursive self-reference as the structure of reality itself.

In 1980, Benoit Mandelbrot at IBM computed what the Vedic seers described in words. The Mandelbrot set is defined by the simplest possible rule: z → z² + c. The boundary has infinite complexity — zoom into any point on the edge and you find the same structures, the same spirals, the same miniature Mandelbrots, forever. The jewel that contains all jewels.

"In the heaven of Indra there is said to be a network of pearls so arranged that if you look at one you see all the others reflected in it."— Avatamsaka Sutra, 3rd century CE

Every artwork generated here is a unique window into a specific coordinate in an infinite mathematical object. The parameters — centre point, zoom level, iteration depth, colour cycle — are the complete description of that view. Save them and the view is reproducible exactly, by anyone, forever. A mathematical certificate of a specific location in infinity.

Indra's Net · Atharva VedaBenoit Mandelbrot · 1980z → z² + cSelf-similar at every scaleJulia setsInfinite complexity
Zone II — The mathematics

z → z² + c — nine characters, infinite worlds

The Mandelbrot iteration is computed for every pixel. Each pixel represents a complex number c = x + iy. We run z_{n+1} = z_n² + c from z_0 = 0. If |z| exceeds 2, the pixel escapes — coloured by speed of escape. If it never escapes, the pixel is inside — pure black.

// Mandelbrot iteration
z₀ = 0
z_{n+1} = z_n² + c, c ∈ ℂ
c ∈ M iff |z_n| ≤ 2 for all n
// Julia sets: z_{n+1} = z_n² + c, z₀ = pixel
// Fractal dimension of boundary ≈ 2
Iteration rule
z²+c
9 characters
Boundary dim.
≈ 2
fractal, not a line
Self-similarity
at every zoom level
Julia sets
one per complex c
Zone III — Your sandbox

Enter the boundary

Toggle between Mandelbrot and Julia. Zoom inward to the edge — mini Mandelbrots appear in the filaments. Drag to explore at each level.

Exploring the boundary
Click anywhere to centre · Scroll to zoom · Parameters saved automatically
Custom colours
Palette presets
Seed: MJ-0000-xxxx
Current design — seed: MJ-0000-xxxx
This window exists nowhere else

Your fractal view is a unique coordinate in an infinite mathematical object. The PDF records the exact zoom, centre, iteration count, and palette.

All eight traditions