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Hydrothermal Pool



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=15804

A visualization of a Triskelion Mandelbrot (parameter-space slice). This is only part of a many-dimensional object, and only studies one critical point (zero). The red, green, and blue components of the color of a point are determined by a weighted average of distance from the three cube roots of unity -- a different cube root for each color. Areas of strong primary color occur in parameter regions where one of these is strongly attracting and quickly draws in zero. In other areas, zero wanders for a while, goes to a fourth attractor, or none of the three cube roots attract strongly if at all.

Minibrots and other Mandelbrotesque shapes are visible, particularly at lower left. Other areas are grey-blue and intricately variegated, or similarly but tinged toward other colors; these are parameter regions with no attractors at all. In yet other areas, intricate borders vie wildly for points; these areas have multiple basins of attraction vying for zero, and the border shapes are indicative of the general shapes produced by the Julia sets for parameters nearby.

If this is just a slice of a many-dimensional object, I wonder what that object looks like.

Thanks.