File:Menger sponge (Level 0-3).jpg
Menger_sponge_(Level_0-3).jpg (800 × 228 pixels, file size: 89 KB, MIME type: image/jpeg)
Captions
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.
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/Time | Thumbnail | Dimensions | User | Comment | |
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current | 19:38, 20 February 2005 | 800 × 228 (89 KB) | Solkoll~commonswiki (talk | contribs) | Re-uploading this, (there was a minor typo in the previous version) |
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- File:Menger sponge (IFS).jpg
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JPEG file comment | File written by Adobe Photoshop¨ 5.0 |
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