Sequence Fractals Part I #6

233.jpg

z^2+c+s_i
si = 1, -1, 1, -1, …
Center:-2.21745+0i , Zoom = 800

Same location as yesterday Sequence Fractals Part I #5, with 10x zoom and 50% more color entropy. This is another two-cycle.

A two cycle means f(f(z_0,c),c)=z_0 \ and \ f_c(z_0) \ne z_0. The second iteration comes back to the start point. The second part of the definition excludes fixed points. f is degree 4 polynomial in z and degree 2 in c. With the fixed start point z0=0 the double iteration in the definition is a degree 8 polynomial in c. It has 8 roots, with 6 left over after removing the fixed points (0 and -3).

Here are the (c-parameter values) of the six two-cycles

2.00:  -3.604653,  0.000000
2.01:  -3.079229,  0.000000
2.02:  -2.217445,  0.000000
2.03:  -0.186836,  0.000000
2.04:   0.044082,  0.464238
2.05:   0.044082, -0.464238
2.00 is Sequence Fractals Part I #4. 2.02 is today’s image. 2.01 is the period 2 bulb (nose) in c = -3, Sequence Fractals Part I #3, and 2.03 is the center of the nose of c = 0, Sequence Fractals Part I #2. 2.04 and 2.05 are the wings above and below the c=0 brot in Sequence Fractals Part I #2.

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