Tool · Playground
Escape-time designer
Build your own escape-time fractal. Pick a family for z_{n+1} = f(z, c) — polynomial, perturbed-polynomial, burning-ship, sin, or exp — tune the exponents, choose Mandelbrot (vary c) or Julia (vary z₀) mode, then click to zoom.
center = (-0.5000, 0.0000i), scale = 1.50e+0
Click to zoom 2× at the cursor.
Family
Mode
Render
What to explore
- Non-integer exponents: n = 2.5 in the polynomial family gives a Mandelbrot-like set with broken rotational symmetry. n < 2 has no bulb cascade.
- z² + c·z (perturb family, n=2, k=1) shifts the cardioid sideways. Try other (n, k) pairs to see how mixing terms reshape the set.
- Burning-shipat n=2 is the canonical “ship”. Crank n up to 4-5 to see its bulbs balloon and split.
- Julia for arbitrary families: not just z² + c — you can ask for the Julia set of sin(z) + c. The shapes are wildly different from quadratic Julias.
The fixed-family Mandelbrot lives at /tools/mandelbrot and Julia at /tools/julia. See /tools/multibrot for the integer-n polynomial family.
FAQ