Sequence Fractals

In mathematics a sequence is an infinite ordered list of numbers. https://en.wikipedia.org/wiki/Sequence

Sequences are cool, I decided to look for ways to combine sequences and fractals.

Of course I can take any topic and wonder how to combine it with fractals so this may not be a brilliant inspiration, rather just the normal inner workings of a fractal addled brain. And actually my short definition of sequence is wrong for multiple reasons. Technically sequences can be infinite or finite and do not have to be numbers. You could have a sequence of turtles. Let’s keep it simple and stick with infinite sequences of complex numbers.

Oops, still not quite there. For practical time and space reasons, we won’t be using the whole infinite sequence, just the first million or so values.

Today’s picture? This is a picture of a particularly messy sequence. The sequence is bounded but does not converge. The picture is a portion of the complex plane with a fuzzy dot for each number in the sequence.