T-square (fractal)

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.
## 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.
## From each of the quadrants of Image 1, 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.

Properties

T-square has a fractal dimension of ln(4)/ln(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.

ee also

*List of fractals by Hausdorff dimension
*Sierpinski carpet