Xaos, a fractal zoomer

In the good old times of my MS days, Dr. Manlapaz introduced us to chaos, Mandelbrot and Julia sets Sierpinski gaskets,the universal Feigenbaum constant and bifurcations. He was the supreme mental terrorist of masters students who did not share his adventurous mind. As a part of his Math 270 class, we were required to program the Mandelbrot set of complex functions, including roots of polynomials using unoptimized Newton's method. As an illustration of the fear he induced in the students, there were teachers|students who have to take Math 270 more than three times!

I did not get a grade of 1.0 but was happy to pass his course. I used a pirated Turbo BASIC program to program my assignment and it took a long time to display the final output on the slow VGA screens of the past! Remember we were only using the lowly 8086, and the 80386. The 486 was just coming into the market. A little later when I was already in my Ph.D. program, I recall a program called Xaos which run amazingly fast, in real time! on the Mandrake 7.2 OS.

Today the Xaos still survives, and it still reminds me of my dear professor. He actually mentioned some speed techniques in programming in BASIC without resorting to assembly.

Enough of the memories. So what is Xaos? It is a fractal zoomer, just a left mouse button press will zoom the figure in the graph window and a right mouse button will unzoom the figure for a wider scale view. Here is the opening screeen, obtained by selecting Applications/Graphics/Xaos.

and here is a zoomed view:

Of course, Xaos gives other interesting regions to explore aside from the well known $$z_{n+1}= z_{n}^2 + c$$. It even saves your animations to a file for playback later. we live it to the reader to explore on his own the fractal world. We don't want to rob you of the joy of wondering what fascinated the geeks of yersteryears.:)