Fractal Lab

Tool

Burning Ship explorer

Escape-time iteration of z ← (|Re z| + i|Im z|)² + c. The absolute values break complex-analytic symmetry, producing the eponymous ship-like feature around c ≈ -1.76 + 0.04 i.

Click to zoom in (shift-click to zoom out). Drag to pan.0 ms

center: (-0.500000, -0.500000)

scale: 3.50e+0

Iteration rule

z_{n+1} = (|Re z_n| + i |Im z_n|)² + c    with    z_0 = 0
expanded:
  Re z_{n+1} = (|Re z_n|)² − (|Im z_n|)² + Re c
  Im z_{n+1} = 2 · |Re z_n| · |Im z_n| + Im c
escape test: stop when |z_n| > 2

Absolute values break complex-analytic structure, so symmetry is only about the real axis.

Background at /fractals/burning-ship.