The Gardens of Atlantis

[Ross Hilbert]

The Gardens of Atlantis



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=17092

Created with the Fractal Science Kit fractal generator. See http://www.fractalsciencekit.com/ for details.

[Kalles Fraktaler]

All your images are fantastic and beautiful.
You have created a really impressive gallery.
It would be nice to get some insight in what these images are made of, is it Mandelbrot or not, etc.
Anyway, thanks a lot for all the images

[Ross Hilbert]

Thanks Kalles Fraktaler!

Many of my works are Mandelbrot or Julia based fractals, but I also generate some IFS/Attractor based images, Kleinian Group fractals, or as in this case, the image is based on a [6,4] Hyperbolic Tiling.

A Hyperbolic Tiling replicates a polygon over the hyperbolic plane (represented by the Poincare disk) in such a way as to form a hyperbolic tiling pattern. The Poincare disk is a model for hyperbolic geometry that maps the hyperbolic plane onto the unit disk. A [p,q] regular tiling of the hyperbolic plane maps a hyperbolic polygon with p sides over the hyperbolic plane such that q polygons meet at each polygon vertex. For example, a [4,5] regular tiling maps 4 sided polygons onto the hyperbolic plane such that 5 polygons meet at each polygon vertex. A regular tiling of the hyperbolic plane exists if and only if (p-2)*(q-2) > 4. So, for example, a [4,5] tiling is possible but a [4,4] tiling is not.

I'll try to remember to give a little info about the image in the future, but if I forget, just pose a question and I'll reply when I can.

Thanks again!