P.S. What happens if at each stage of the 3D snowflake, the new pyramids are derected *inward* instead of being erected outward? The resulting geode could for viewing be sliced open or subjected to inversion in a the circumscribed sphere. —Dan
On Mar 16, 2016, at 11:25 PM, Dan Asimov <asimov@msri.org> wrote:
Maybe it's the yellow color, but this everted fractal reminds me perforce of a durian fruit.
—Dan
On Mar 16, 2016, at 6:42 PM, Bill Gosper <billgosper@gmail.com> wrote:
If each octant of this fractal is everted, so that all eight corners wind up in the center, we do not see eight "corner reflectors", but rather a hint of what BBM was trying to describe. gosper.org/unstella.svg <http://gosper.org/unstella.svg> except that the little octahedra should be little gobs of razor blades. The true limiting fractal here is the disjoint union of six copies of itself placed on the vertices of its bounding octahedron, and then scaled by 1/2. The intersection of this figure with its bounding octahedron is eight Sierpinski gaskets. --rwg