Title: Alternative ways of creating the Mandelbrot set Post by: twinbee on March 28, 2008, 04:03:24 AM I didn't realise there was another way of creating the set until I found this (http://science.slashdot.org/comments.pl?sid=11233&cid=346043):
I quote: Quote You don't need imaginary numbers to define the mandelbrot set. Start with point (x[1],y[1]). When you do the iterations, x[next] = x[previous]^2 - y^2 + x[1] and y[next] = -y[previous]^2 + y[1]. And the image shown is most definitely a rendering of the mandelbrot set. Unfortunately, he lost me at the y^2 bit. Perhaps he meant y[1] (which doesn't work btw)? My attempt at reproducing the method has failed so far: Code: double nx; double ny; Any ideas of what needs to be changed? And to to keep on topic generally, are there any other simple ways of creating the Mandelbrot set? Title: Re: Alternative ways of creating the Mandelbrot set Post by: juharkonen on March 29, 2008, 01:10:17 PM Calculations with complex numbers can always be translated to calculations in real numbers (using the definition of complex numbers). For the logistic map z(n+1) = z(n)^2 + C used to calculate the Mandelbrot set, this translates to x(n+1) = x(n)^2 - y(n)^2 + xC y(n+1) = 2*x(n)+y(n) + yC where C = (xC, yC) = xC + i*yC and z(n) = (x(n), y(n)) = x(n) + i*y(n). Comparing to your reference, it seems that the calculation of the y coordinate is incorrect. I didn't test this one neither but I hope you got the idea. I don't know about other ways to calculate the Mandelbrot set and I wouldn't say this essentially differs from the calculations using complex numbers - it's just a different representation of the same calculations. Title: Re: Alternative ways of creating the Mandelbrot set Post by: GFWorld on March 30, 2008, 11:17:11 AM Twinbee - thank´s for your visit and comments - you picked up here some of my own favorites :)
*** FeSt 8 - I lost it, but I am sometimes trying to return back , knowing about the impossibility at last :-))) It was created with Fe Sterlingware / Twister Weed , playing around here with CAbs , CAbs 2 & CSin Functions ... *** >These 3 also come very close: Mb1/mb4.html / Formula by Paul W.Carlson Fr1/fe126.html / Fe JT_Rosegarden Fr1/fe116.html / Fe Sierpinskie Formula by Rico Wack *** >These aren't as good as the above, but still really nice: Fr1/fe100.html / Fe JT_Dahlia UF/7.html / UF Sorensen Cubic - one of *my* places starting for Mini´s :-) UF/120.htm / UF Julia Tricorn Fr1/fe162.html / Fe JT_Venice Fr1/fe181.html / Fe Newton Var by Girvan Mut/Mut23.htm / MutatorKammer Alternating Fractals CM & Orbit Traps Margit Title: Re: Alternative ways of creating the Mandelbrot set Post by: cKleinhuis on March 30, 2008, 03:29:49 PM as far as i know the above method works for julia sets, did you paint mandelbrot fractals with that rendering loop ?
Title: Re: Alternative ways of creating the Mandelbrot set Post by: lycium on March 30, 2008, 03:36:21 PM Comparing to your reference, it seems that the calculation of the y coordinate is incorrect. I didn't test this one neither but I hope you got the idea. I don't know about other ways to calculate the Mandelbrot set and I wouldn't say this essentially differs from the calculations using complex numbers - it's just a different representation of the same calculations. different and less meaningful representations, agreed. |