On 2016-03-18 06:21, Tom Karzes wrote:
If I understand this correctly, it looks like the surface tetrahedrons touch each other starting at the third iteration, completely sealing off chambers below the surface which continue to be filled in as the iterations progress. And though the surface makes contact with itself, it never actually passes through itself, is that right?
Yes. The fractal boundary reminds me of the inside of a crab.
Question: Is there a 4D analog to the snowflake curve, based on 4D simplexes? If so, would the surface of this curve pass through itself?
Tom
Sounds plausible, but 4space is very spacious.
George Hart been here, done this eight years ago. --rwg http://www.georgehart.com/ProceduralGeneration/Bridges08-Hart10pages.pdf
Bill Gosper writes:
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.
producing a strong echo while flapping in the breeze.
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