On 2016-03-17 07:07, Mike Stay wrote:
Nice! A cross-section perpendicular to an axis 3/4 of the way along the length gives the "box fractal". It would be fun to see an animation of the slices. In that vein: https://www.simonsfoundation.org/multimedia/mathematical-impressions-the-sur... [1]
Mathematica is developing a "region calculus", e.g., gosper.org/cubeslice.png [2] that might soon facilitate this. --rwg
On Wed, Mar 16, 2016 at 6:42 PM, Bill Gosper <billgosper@gmail.com> wrote:
Most of you know that it makes a cube: gosper.org/3dsno.png at least if you unite closed solids. The sequence of boundaries converges to a fractal that so distracted Mandelbrot that he neglected to mention its cubicalness. 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 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
Metallic instances of the "eight corner reflectors" figure are hung from boat masts as radar reflectors. _______________________________________________
Links: ------ [1] https://www.simonsfoundation.org/multimedia/mathematical-impressions-the-sur... [2] http://ma.sdf.org/gosper.org/cubeslice.png