T-Square (fractal)

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

It can be generated from using this algorithm:

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

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

T-Square has a fractal dimension of 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
• Koch snowflake
• T-square
• Sierpinski carpet

 

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