T-square (fractal)
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This article is about a two dimensional fractal in mathematics. For other uses, see T-square (disambiguation).
In mathematics, the T-square is a two-dimensional fractal. As all two-dimensional fractals, it has a boundary of infinite length bounding a finite area. Its name follows from that for a T-square.
[edit] Algorithmic description
It can be generated from using this algorithm:
- Image 1:
- Start with a square.
- Subtract a square half the original length and width (one-quarter the area) from the center.
- Image 2:
- Start with the previous image.
- Scale down a copy to one-half the original length and width.
- The previous image's square has four equal quadrants. From each of the quadrants, subtract the copy of the image.
- Images 3-6:
- Repeat step 2.
The method of creation is rather similar to the ones used to create a Koch snowflake or a Sierpinski triangle.
[edit] Properties
T-square has a fractal dimension of log(4)/log(2) = 2. The black surface extent is 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.
