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Mandelbrot set deep zoom

Elephant Valley

Elephant Valley sits along the right edge of the main cardioid of the Mandelbrot set, around c ≈ 0.27 + 0.006i. Zooming in reveals trunk-and-tusk spirals that look like a parade of elephants.

Center:
0.27931499 + 0.0093967421i
Zoom:
3.950e-3
Palette:
fire
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About Elephant Valley

Elephant Valley runs along the eastern boundary of the Mandelbrot set's main cardioid, near c ≈ 0.27 + 0.006i. Where Seahorse Valley produces tightly wound double spirals, Elephant Valley produces broader curls that — at the right zoom — really do look like a procession of cartoon elephants, complete with trunks and tusks. The valley is also a great place to find period-doubling bifurcations: bulbs branching off the main cardioid, each with its own family of decorations. Mandelbro opens this view with the fire palette and a higher iteration count to keep boundary detail crisp as you zoom.

About the Mandelbrot set

The Mandelbrot set is the set of complex numbersc for which the iteration zn+1 = zn2 + c does not escape to infinity. Its boundary is a fractal of infinite detail: every region you zoom into reveals new spirals, dendrites, and miniature copies of the entire set. Elephant Valley is one of the most recognizable patterns in this boundary.

How Mandelbro renders this view

At this zoom level, Mandelbro uses standard double-precision rendering with a parallel pool of Web Workers — every CPU core in your device runs the escape-time algorithm in parallel on a slice of the viewport. Push the zoom another twelve orders of magnitude in and the renderer automatically switches to its perturbation pipeline, which uses one high-precision reference orbit to keep deep zooms sharp. See how Mandelbro works for the full explanation.

Other famous Mandelbrot locations