T-Square Fractal

The T-Square Fractal starts from a single square. Then, on each iteration, four smaller squares are placed at the corners of every existing square. Repeating that simple rule builds up a pattern of overlapping squares that quickly becomes much more intricate than the starting shape suggests.

In this implementation, the most important parameter is the resize ratio between iterations. A ratio of 0.5 gives the classic version, but changing that value lets the pattern open up or crowd together in different ways.

Algorithmically, it is very direct:

drawSquare(center, size);

if (depth < iterations) {
  drawTSquare(topLeftCorner, size * ratio);
  drawTSquare(topRightCorner, size * ratio);
  drawTSquare(bottomLeftCorner, size * ratio);
  drawTSquare(bottomRightCorner, size * ratio);
}

Even though it is built from squares, the negative space between those squares can start to echo the triangular gaps that appear in the Sierpinski Triangle. It also belongs in the same recursive family as the Sierpinski Carpet, where a very small placement rule creates a much larger geometric structure.