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)
   
 OFFSET    

0,1
    LINKS    

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).

    FORMULA    

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

at

7 comments:

  1. PatafractalWednesday, 12 April, 2017

    Less Trump
    More Fractals
    Make Mandelbrot Great Again !

    ReplyDelete
  2. Vleeptron DudeWednesday, 12 April, 2017

    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.

    ReplyDelete
  3. Vleeptron DudeWednesday, 12 April, 2017

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

    ReplyDelete
  4. PatafractalWednesday, 12 April, 2017

    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.

    ReplyDelete
  5. SADLOVESaturday, 10 June, 2017

    too late ... Mandelbrot *is* super-great again! You got a cell phone? a smart phone? open it up (carefully!) and look at its antenna.
    goldenslot
    gclub online
    บาคาร่า online

    ReplyDelete
  6. Vleeptron DudeWednesday, 28 June, 2017

    NaRong

    r u carbon-based or silicon-based intelligence?

    r u Thai? My sadness for the passing of Bhumipol.

    Could you maybe get rid of the "Lese Majeste" law (and long Thai prison sentences for those who dare commit this odd crime)?

    Please ignore if you are Nepalese or Papiementu.

    ReplyDelete
  7. lovely boyFriday, 20 November, 2020

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    ReplyDelete