
Blog Entry (c) Saturday, September 14, 2024, The Mandelbrot Set by James Pate Williams, Jr. A Simple Fractal Self-Similar Curve





Unfortunately, I can only find the preceding executable applications and no source code. These programs date back to 2001 and 2002 while I was a graduate student in software engineering and computer science at Auburn University. I seem to recall that these apps were created using Win32 C or C++.
Solve for a real root of the equation
f(x)=log6l(5+x)+log6l(x)=0
First we test our log6l(x) function
log6l(12) = 1.386853
log6l(36) = 2.000000
x = 0.1925824036
f = 0.0000000000
We use an evolutionary hill-climber and the solution of the quadratic equation to solve the easy problem below:
Solution of f(a,x)=sin(sqrt(ax-x^2))=0
Subject to the constraint x+y=100
Where x and y are the two roots of
g(a,x)=ax-x^2-n*n*pi*pi=0
and n=15
a = 100.347888933988
x = 32.947113268776
y = 67.400775665213
g = 0.000000000000
s = 100.347888933988
runtime in seconds = 43.730000