Tool
Tricorn explorer
Anti-holomorphic iteration z ← conj(z)² + c. The boundary has three-fold symmetry instead of the Mandelbrot’s reflection symmetry.
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center: (-0.300000, 0.000000)
scale: 3.60e+0
Iteration rule
z_{n+1} = conj(z_n)² + c with z_0 = 0
expanded (z = x + iy, conj(z) = x − iy):
Re z_{n+1} = x² − y² + Re c
Im z_{n+1} = −2 x y + Im c
escape test: stop when |z_n| > 2Anti-holomorphic (uses the complex conjugate), giving three-fold symmetry instead of reflection symmetry.
Background at /fractals/tricorn.