Fractal Zoom Explorer

Maths Club โ€” Click anywhere to zoom in 3ร—

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๐Ÿ” How to explore
Click anywhere on the image to zoom in 3ร— at that point. Use Zoom Out to zoom 3ร— out from the current center. Type coordinates into the center field (e.g. -0.745, 0.113) and press Zoom In โ€” an orange rectangle will preview the target area. The most interesting detail is at the boundary between black (inside) and colour (outside)!
๐ŸŽจ How the colour works
Each pixel is a number c on the complex plane. We iterate the formula and count steps to "escape." Smooth colouring (ฮผ = n + 1 โˆ’ log(log|z|)/log 2) maps step count to the selected palette. Points that never escape are black โ€” they're inside the fractal.