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 NCB Deposit  # 157

Dr. Cye Waldman
cye@att.net

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Animated Members of the Mandelbrot Family of Plane Curves

 
macacu stamp

The evolution of fractals for two Julia sets and the Mandelbrot set.......................................


animation1


animation2




Mandelbrot

We also have interesting Mandelbrot/Julia trap demonstrations in NCB Deposit #156.

Lambda Plane
classic

Inverse Lambda Plane
inverse
  The lambda plane defined by the recursion formula is . . . . . .
equation

In the animation below,  p is varied from  1/5  to  5 in increments of  1/5  and the regular  (+ p) and inverse (-p ) forms are overlaid.   Of course, other variations are possible as well, such as replacing  ( 1 - z ) by  ( z - 1 )  or  ( 1 + z ).  Then too, you can exponentiate the  z- terms.  There is no end to this madness."
lambda animation

References
SciAm85
August, 1985
Other  Fractal deposits in the NCB :
< http://curvebank.calstatela.edu/fractal2012/fractal2012.htm >
< http://curvebank.calstatela.edu/fractal/fractal.htm >

Other Related Waldman spirals in the NCB:
The Fibonacci and Pseudospirals: < http://curvebank.calstatela.edu/waldman6/waldman6.htm >



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