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| > 2Absolute values break complex-analytic structure, so symmetry is only about the real axis.
Background at /fractals/burning-ship.