Formula f(z,c) Start value s Image Remark
0.0 the new top formula is a parametrized one: z2 + c + alpha/c,
which results in an animation you can watch here, or on youtube or you can download it.
The animation shows the parametrized formula between the parameters alpha=-2 to alpha=2.
For alpha=0 the formula is the classic Mandelbrot set. This is, where the animation "stops" for one second.
0.0 a double apple manikin with connected apple manikins.
A simple formula derived from the formula of the classical Mandelbrot set: z2+c.
This simple formula I obtained playing with c-transformations.
0.0 a variation of the formula above.
Seeing the pattern in the formula results in the next formula c10+1/c10.
0.0 a ring of 20 pairwise connected apple manikins
0.0 another simple formula, close to the first one
0.0 variation with more apple manikins
0.0 a triple, function found by playing with z-transformations on z2+c
0.0 the same triple with a different rendering method
0.0 result of a calculation error calculating the above formula.
Just a one was missing.
Amazingly very look a like images, such look a like pairs with different formulas I call twins.
1.0 double apple manikin
-0.25z^2c^2+zc 1.0 another double apple manikin
rendered with "BeamBrown2N" rendering method
rendered with mathematical rendering method
see the render page
-1.0 double apple manikin, attached to island
-0.099105672621 same formula, double apple manikin close by to the double apple manikin above.
You can watch this function with changing start values on youtube
0.0 amoeba
1.0 flower nova
0.82471921 4 spiral Ferguson nova
rendered with mathematical rendering method
see the render page
0.0 nova with big apple manikins on tip
1.0 apple manikin with circle form
0.83677334 flower amoeba, a bit weird
0.81063034 flower apple manikin
1.224489795918 apple manikins within a circle