T-square (fractal)
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Lua error in package.lua at line 80: module 'strict' not found. 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.
Algorithmic description
It can be generated from using this algorithm:
- Image 1:
- Start with a square. (The black square in the image)
- Image 2:
- At each convex corner of the previous image, place another square, centered at that corner, with half the side length of the square from the previous image.
- Take the union of the previous image with the collection of smaller squares placed in this way.
- 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.
Properties
T-square has a fractal dimension of ln(4)/ln(2) = 2.[citation needed] 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 fractal dimension of the boundary equals .
See also
- List of fractals by Hausdorff dimension
- Sierpinski carpet
- The Toothpick sequence generates a similar pattern
References
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