File:Menger sponge (Level 0-3).jpg

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Menger_sponge_(Level_0-3).jpg (800 × 228 pixels, file size: 89 KB, MIME type: image/jpeg)

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This image is an illustration of the recursive process of generating a Menger sponge, which is a fractal object. It shows the first three iterations of an infinite process. The illustration was created by using a simple "Lindenmayer system" (L-system).

The number of cubes at a given iteration is , where is the number of iterations performed on the first cube:

Iter. Cubes Cumulative Sum
0 1 1
1 20 21
2 400 421
3 8,000 8,421
4 160,000 168,421
5 3,200,000 3,368,421
6 64,000,000 67,368,421

At the start, no iterations have been performed so . The image shows a total of 8,421 cubes (the sum of all four steps).

See also:


Image: User:Solkoll.
Public domain This work has been released into the public domain by its author, Solkoll. This applies worldwide.

In some countries this may not be legally possible; if so:
Solkoll grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


More 3D fractals from my tool:

All freaktal images are from self-written tools. Linear fractals from my : "3D IFS studio" and "3D DTIFS" (dragon trees), non-linear IFS from "3D RJIFS" (3D rev Julia).

See also: Solkoll & Solkoll 2D

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Date/TimeThumbnailDimensionsUserComment
current19:38, 20 February 2005Thumbnail for version as of 19:38, 20 February 2005800 × 228 (89 KB)Solkoll~commonswiki (talk | contribs)Re-uploading this, (there was a minor typo in the previous version)

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