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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.
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 fractal dimension of the boundary equals .
- List of fractals by Hausdorff dimension
- Sierpinski carpet
- The Toothpick sequence generates a similar pattern
- Hamma, Alioscia; Lidar, Daniel A.; Severini, Simone (2010). "Entanglement and area law with a fractal boundary in topologically ordered phase". Phys. Rev. A 82. doi:10.1103/PhysRevA.81.010102.
- Ahmed, Emad S. (2012). "Dual-mode dual-band microstrip bandpass filter based on fourth iteration T-square fractal and shorting pin". Radioengineering 21 (2): 617.