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12 April 2017

Menger Sponge / Cantor Dust

click to enlarge maybe

A212596         Number of cards required to build a Menger sponge of level n in origami.         1
    12, 192, 3456, 66048, 1296384, 25731072, 513048576, 10248388608, 204867108864, 4096536870912, 81924294967296, 1638434359738368, 32768274877906944, 655362199023255552, 13107217592186044416, 262144140737488355328, 5242881125899906842624
(list; graph; refs; listen; history; text; internal format)


Table of n, a(n) for n=0..16.

CTRL Byte, 2010-04-13, Menger Sponge Construction

ELJJDX, Choux romanesco, vache qui rit et intégrales curvilignes, Am-stram-gram, ticket-ticket-bus-et-tram (French)

Nick Hamblet, Σidiot's Blog, 2009-03-01, Counting Cards

Michel Lucas, Défi 66 000 tickets (French)

Dr. Jeannine Mosely, The Institute For Figuring, Business Card Menger Sponge

Nicholas Rougeux, Mengermania, Instructions

Wikipedia, Menger sponge

Index entries for linear recurrences with constant coefficients, signature (28,-160).


a(n) = 4*(8^n + 2*20^n) = 2^(2*n+3)*5^n+2^(3*n+2).


Patafractal said...

Less Trump
More Fractals
Make Mandelbrot Great Again !

Vleeptron Dude said...

too late ... Mandelbrot *is* super-great again! You got a cell phone? a smart phone? open it up (carefully!) and look at its antenna. These itty-bitty antennæ are Mandelbrot fractals. A fractal antenna (unlike old-fashioned traditional antennæ) can tune into a very big spectrum of electromagnetic frequencies!

Vleeptron and moNGO are working on the Less Trump thing. Watch this space.

Vleeptron Dude said...

ADDENDUM: VAMRI (Vleeptron Advanced Mathematical Research Institute) just found this supercaliafragialisticexpialidocious Cantor Dust!

Patafractal said...

Cantor and his little monsters – if I am not mistaken then Benoit (Baruch ?) Mandelbrot used this as the base idea for his fractals.
Cantor went mad when he thought about Infinity. Poor bugger.
Did you know that you can find those little Cantor Monsters in a Bach Cello Suite ?

I would like to remind the public that you can do this stuff yourselves. There are various free 3D fractal generators out there. You will need some time and patience but it will be worth it. Making Fractals is better than Making War.