Title: Mobius IFS on the Poincare disk Post by: arki on March 20, 2016, 11:27:27 PM The fractal-like image below is made of 8 tansformations, 2x2 complex matrices acting on the complex plane via linear fractional transformations. Four of them are from the group SU(1,1), for other are disk contractions. In fact they are the same as the first four, but with imaginary parameter. The method of generation is described in my Mathematica notebook Oscillator semigroup, quantum measurements, and fractals on squeezed States (http://arkadiusz-jadczyk.eu/docs/sqeezed_notebook_a.nb) that I prepared to accompany the forthcoming paper. It is the last example in the notebook. The image looks like 3D (spikes), but it is 2D only.
(http://arkadiusz-jadczyk.eu/images/w8.jpg) The IFS is made of 100 000 000 points. Using Mathematica one has to wait several minutes. But already 100 000 points are sufficient to get a rough idea about the shape. Changing parameters will produce other patterns. I do not know if this kind of fractal-like IFS has already been discussed somewhere. P.S. The same factory, but with different parameters: (http://arkadiusz-jadczyk.eu/images/w82.jpg) Title: Re: Mobius IFS on the Poincare disk Post by: fuglaro on May 13, 2016, 12:20:13 AM Nice fractals, Arki! |