National
          Science Foundation
National Curve Bank

Variable Orbit Trap


Animated Members of the Mandelbrot Family of Plane Curves

Deposit #156

Dr. Cye Waldman

mandelbrot

Waldman writes:
"There is some interesting math associated with calculation of the orbit trap, which requires the shortest distance between the iterated Mandelbrot point and the orbit trap. The brute force method is to do two 'for' loops to cover each of the iterated points on the plane and determine the shortest distance to the trap. Based on something I developed for the fractal tiling I've done, I was able to accomplish this 'all-at-once' (no for loops; vectorized code) using some fancy matrix work based on the Kronecker tensor product, cleverly rewritten to be a Kronecker sum. The problem with the method is that these matrices can be huge and one must resort to the for loops, as I did for the fractal spiral orbit trap."

The animation below shows .......................................

fractal orbit trap

The concept..............................


  CYE:   Save this space but what to you suggest I write here?????????


trapzoom



complex
                                                          plane




Equations??????????????????????????

References
SciAm85
August, 1985
Other  Fractal deposits in the NCB :
< fractal2012.html >
< fractal.html >

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



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