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Description
A Mandelbrot Set colored with the accumulation of a Mandelbrot Zoom, into an upper pocket of the Elephant Valley. The Mandelbrot Zoom was converted into a horizontal banner using the formula z = exp(z) + location, and then used as background for the Mandelbrot Set per logarithm formulas. The composite mapping from the Mandelbrot Zoom to every band is conformal, as it is the image of a polynomial (z_0 = 0, z_n=z_(n-1)^2+z), and in fact holomorphic, since the number of iterations to every band is finite. The colors of the Mandelbrot Zoom banner were dampened to 70% saturation to include a secondary coloring for the Mandelbrot Set, to delinate structures on the Mandelbrot Set.

See www.flickr.com/photos/arenamon… for a collage of horizontal banners.

Description
A Mandelbrot Set colored with the accumulation of a Mandelbrot Zoom, into an upper pocket of the Elephant Valley. The Mandelbrot Zoom was converted into a horizontal banner using the formula z = exp(z) + location, and then used as background for the Mandelbrot Set per logarithm formulas. The composite mapping from the Mandelbrot Zoom to every band is conformal, as it is the image of a polynomial (z_0 = 0, z_n=z_(n-1)^2+z), and in fact holomorphic, since the number of iterations to every band is finite. The colors of the Mandelbrot Zoom banner were dampened to 70% saturation to include a secondary coloring for the Mandelbrot Set, to delinate structures on the Mandelbrot Set.

See www.flickr.com/photos/arenamon… for a collage of horizontal banners.