T-Square (fractal)

From Biocrawler, the free encyclopedia.

The T-Square is a fractal curve of infinite length inside finite area.

It can be generated from using this algorithm:

1. Image 1:
   1. Start with a square.
   2. Subtract a square half the original length and width (one-quarter the area) from the center.
2. Image 2:
   1. Start with the previous image.
   2. Scale down a copy to one-half the original length and width.
   3. The previous image's square has four equal quadrants. From each of the quadrants, subtract the copy of the image.
3. Images 3-6:
   1. Repeat step 2.

The method of creation is rather similar to the ones used to create a von Koch curve or a Sierpinski triangle.

The fractal dimension of the thing is log(4)/log(2) = 2. The black surface extent almost everywhere in the bigger square, for, once a point has been darkened, it remains black for every other iteration ; however some points remain white. The limit curve is a fractal line, of fractal dimension 2.

See also:

• Fractal
• von Koch curve
• T-square
• Sierpinski carpet

Wikipedia (http://en.wikipedia.org/wiki/Main_Page) T-Square_(fractal) (http://en.wikipedia.org/wiki/T-Square_(fractal)) version history (http://en.wikipedia.org/w/index.php?title=T-Square_(fractal)&action=history) GNU Free Documentation Lizenz (http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License) CC-by-sa (http://creativecommons.org/licenses/by-sa/2.5/)

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