I'm not a mathematician, but a part time artist, and I enjoy drawing patterns. I came up with this drawing a couple years ago:
Someone may have come up with this before me, I wouldn't be surprised. I don't know if it's a fractal, but as it is drawn it branches out in a way which reminds me of fractals. I'd like to know if anyone has any explanation for this type of pattern or knows of similar patterns that I could compare it to. Thanks.
The rules for the design are as follows:
- A drawn arch ends as it intersects any part of another arch.
- As an arch [A] completes one quarter of a circle's circumference, (if it is not at an intersection) it branches out into two more arches, where one branch [B] continues to complete another quarter of the same circle's circumference and the other branch [C] moves out in a reflected direction described by an imaginary axis extending from the end of arch [A]
The first step in drawing the design is to select a center within four quadrants, having a horizontal and vertical axis. Four initial archs branch out from the center in a circular curve, connecting (0,0) to (1,1) in the first quadrant, (0,0) to (-1,1) in the second quadrant, (0,0) to (-1,-1) in the third quadrant, and (1,-1) in the fourth quadrant. It's easier to understand when shown through a visual representation:
As it is drawn it seems to develop squares at the corners or existing squares.