Sequence Fractals Part III #28

$ z^2+c+s_i$
s₀=0.0, s_i+1=s_i²-0.5
Center:-0+0i; Zoom = 0.5

Here the sequence is generated much like orbits of the ubiquitous z^2+c fractals.

This looks similar to the quadratic case when you start someplace other than the critical point.

If we had seeded the sequence at exactly the fixed point (so that the sequence is a single repeated value) then we get a full Mandelbrot set, shifted -0.37. When we start anywhere else, the sequence bounces around a little before settling down. With that early bouncing, some orbits that would otherwise converge get knocked out to infinity.

There are also a few points, harder to identify, that would have escaped that get pushed into the capture set.

Where I live, this summer is on track to be the hottest summer ever. Now we are at the start of August, which has traditionally been the hottest month of the year. I am not enjoying the heat at all. However, I do enjoy generating fractals with the hot palette.