Where all three basins meet — fractal complexity without end.
Near the origin of Newton's z³ − 1 fractal the three basin boundaries converge at a triple point. Zooming in reveals self-similar spirals and smaller triple points at every scale. The boundary is a nowhere-differentiable curve whose Hausdorff dimension exceeds 1.
Real axis (Re)
0
Imaginary axis (Im)
0.58i
Zoom
6×
Max iterations
80
Complex address
A classic Mandelbrot region filled with curling seahorse-like spirals.
Mandelbrot SetA perfect miniature copy of the entire Mandelbrot set, floating in the deep.
Mandelbrot SetA dense spiral basin where bifurcating arms fold into one another.
Mandelbrot SetForked filaments branch outward like a high-voltage tree frozen in mid-strike.
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