----- Original Message -----

From: Hiram Berry

To: Fractint and General Fractals Discussion

Sent: Monday, March 01, 2004 7:03 PM

Subject: [Fractint] Orbit Fractals with an Arbitrary Formula

Is it possible to get fractint to plot these and if so how?  Fractint seems to have specialized orbit types like the Henon attractor, but I want to specify the formula.  IOW the "formula" type iterates over the screen pixels in an orderly gridlike fashion, but I want to go from pixel to pixel by iterating Pixel_new = F (Pixel_old) and mark the pixel each time.  I found this process that seems to generate continuous(with sufficient iteration) fractal curves that look like wads of string with knots in random places (with greater iteration count, the large-scale length of the curve grows, but less than proportional to the number of iterations, and backfilling occurs at the same time at seemingly random locations so the curve is probably dense):

 

x(n) = summation[m=1 to n]( sin(f(n)) * n^-a)

y(n) = summation[m=1 to n]( cos(f(n)) *n^-a)

 

where a is a constant between 0 and 1.  One f that gives a fractal curve (briefly described above) is sqr, while  f=log gives a smooth spiral.  I'd like to plot these with fractint which has deep zooming capabilities, instead of the program I used which does not, and which failed at around 40000 iterated points.  I know about the orbit screen in fractint, but it seems to me that if I use that with a "formula" type it will run the hundreds of thousands of iterations for every single pixel of the screen until the maximum iteration count is hit.  That would take much too long.  Is there some arcane .par magic to get fractint to display an orbit generated from only one point instead of the main screen?

 

Hiram Berry

 

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