Algorithmic worlds 


Search blog posts20130609 Variations on Nova 20130512 Two new gigapixel images 20130428 Lattes Julia sets 20121021 3d hyperbolic limit sets 20120701 Fractal sea creatures 20120624 Nicholas A. Cope 20120616 3d printed Julia set 20120506 Pep Ventosa 20120406 Fractal automata 20120330 Periodic Julia patterns 
BlogA blog about algorithmic art and fractal aesthetic. Click here to subscribe to the RSS feed. October 21st 2012 3d hyperbolic limit setsVladimir Bulatov released a few very nice videos of 3d limit sets of hyperbolic group actions. Two of them are displayed below, but be sure to check his youtube channel for more.
And here are some explanations about what I understand of what these sets are. The hyperbolic space in 4 dimensions has a "Poincaré ball model", analogous to the Poincaré disk model in 2 dimensions, in which it is represented by a 4dimensional ball. The boundary of the 4dimensional ball is a 3dimensional sphere. Now consider a discrete group of isometries of the 4dimensional hyperbolic space and the associated orbit of a point. Points in the orbit might accumulate near certain points of the 3sphere. The points for which this occur form the limit set of the group action. Vladimir used a stereographic projection to map these subsets of the 3sphere back in Euclidean 3dimensional space. When the set gets deformed, either the group or the stereographic projection is modified.


