Agreed, but while the notation's simple, the iterative effect is hard to follow -
it's like a spinning rod, angle doubled and length squared each iteration, with a rod of fixed length and angle added to it each iteration (if the spinner is facing away, it gets shorter, but if towards, it gets longer). Iterate til it goes over 2. If it doesn't then it's in the Set (or maybe you need to iterate more...). [that's my current understanding]
It's pretty clear to me that I can't visualize what it will do over a few iterations (apart from simple cases) - and I sure can't see how it would produce self-similar (ie fractal) shapes. Agreed that that's amazing.
it's like a spinning rod, angle doubled and length squared each iteration, with a rod of fixed length and angle added to it each iteration (if the spinner is facing away, it gets shorter, but if towards, it gets longer). Iterate til it goes over 2. If it doesn't then it's in the Set (or maybe you need to iterate more...). [that's my current understanding]
It's pretty clear to me that I can't visualize what it will do over a few iterations (apart from simple cases) - and I sure can't see how it would produce self-similar (ie fractal) shapes. Agreed that that's amazing.