T-square (fractal)

In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing instrument known as a T-square. In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing instrument known as a T-square. It can be generated from using this algorithm: The method of creation is rather similar to the ones used to create a Koch snowflake or a Sierpinski triangle, 'both based on recursively drawing equilateral triangles and the Sierpinski carpet.' 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 log ⁡ 3 log ⁡ 2 = 1.5849... {displaystyle extstyle {{frac {log {3}}{log {2}}}=1.5849...}} . Using mathematical induction one can prove that for each n ≥ 2 the number of new squares that are added at stage n equals 4 ∗ 3 ( n − 1 ) {displaystyle 4*3^{(n-1)}} .