Fractal Photo Tiler Mapping Lab

Bitmap mapping over Mandelbrot and Julia escape bands. The image follows the escaped orbit — not the screen coordinates — so it repeats with the fractal’s own dynamics.

Drag to pan · mouse wheel to zoom at the pointerStarting…

Fractal

Julia c — realJulia c — imaginary

Complex-plane half width

First visible escape band

Maximum iterations

Anti-aliasing

Fractal rotation

Bitmap pair

Main texture (e.g. column.png)

Cap texture (e.g. columnCap.png)

Export sizeScreen ratio

The cap is used only by the first visible escape band. The main image covers all later bands. For seamless results, author a 2:1 or 4:1 texture whose bottom is half the scale of its top.

Mapping equation

Classic render mix

Blend mode

Classic palette

zₙ₊₁ = zₙ² + c

u = fract(atan2(z.y, z.x) / 2π + phase + rotation)

v = clamp(2 × (ln(400) − ln|z|) / ln(400), 0, 1)

iter = min  → Cap texture
iter > min  → Main texture

u wraps horizontally around the escaping orbit. v uses logarithmic escape overshoot. The period-doubling of z² produces the nested image structure.