National Science Foundation
National Curve Bank

Animated Members of the Mandelbrot Family of Plane Curves

Deposit #157

Dr . Cye Waldman


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 :
< ..//fractal2012/fractal2012.htm >
< ..//fractal/fractal.htm >

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

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