Sequence Fractals Part IV #19

364.jpg

z^2+c*s_i
s0=0.4, si+1=-0.5*si2+2.8
Center:0.0311229+0.2895398i; Zoom = 105000

A zoom into yesterday’s picture Sequence Fractals Part IV #18

I had put this formula into a spreadsheet and generated the first forty values. There were no patterns, It appeared to be a chaotic sequence. In other situations a chaotic sequence leads to “jigsaw puzzle fractals”. Long story short, the sequence is slowly converging to a long cycle. When I extended the spread sheet to 300 rows the sequence appears to be a freshly-bifurcated 32 cycle.

If one were to combine the 32 steps like we did with 2-cycle sequences, we would get a billion degree polynomial. As ridiculous as that number sounds, the pictures do seem normal, about what you would expect from a polynomial.

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