||This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (May 2014) (Learn how and when to remove this template message)|
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 T-square fractal 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.