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SARATH THARAYIL
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IGARATIPO: AMAZON TRIBUTARIES
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Mandelbrot & Julia

Jun 6, 2026

The Mandelbrot set is the set of complex c for which z→z²+c does not escape to infinity. Points just outside escape at different speeds — that escape time, smoothly coloured, reveals infinite boundary complexity. Every point in the Mandelbrot set corresponds to a connected Julia set — hover to see yours.

c = -0.7 + 0.27i

Scroll to zoom · Drag to pan · Hover to preview Julia set at cursor point.

/ NOTES
THE ITERATION

z₀ = 0, z_(n+1) = z_n² + c. If |z| never exceeds 2 within N iterations, c is in the set. Smooth colouring: n + 1 − log₂(log₂|z|) removes banding at the bailout.

JULIA SETS

For any fixed c, the Julia set is the boundary of points z₀ whose orbits escape. Points inside the Mandelbrot cardioid produce connected Julias. Points outside produce Cantor dust. Hover over the Mandelbrot to explore.

WHAT TO TRY

Zoom into the boundary between black and coloured regions — this is where infinite detail lives. Hover along the main cardioid edge to see Julias transition from connected to disconnected. Increase iterations to reveal more structure.