Logo by Trifox
News: Visit the Fractalforums.com User Gallery
 
*
Welcome, Guest. Please login or register. January 09, 2009, 01:46:45 AM


Login with username, password and session length



Pages: [1]
  Print  
Author Topic: Alternative ways of creating the Mandelbrot set  (Read 233 times)
0 Members and 1 Guest are viewing this topic.
twinbee
Fractal Conqueror
*******
Posts: 88


View Profile WWW
« on: March 28, 2008, 04:03:24 AM »

I didn't realise there was another way of creating the set until I found this:

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;
double ox=0.4; double oy=0.5;  // Initialize to any numbers? (these chosen at random)
double px=ox; double py=oy;

for (int n=0; n<100000; n++) {
nx = pow(px,2.0) - pow(oy,2.0) + ox;
ny = -pow(py,2.0)              + oy;

px=nx; py=ny;

int drawx=(int)(nx*100.0 + 400);   // Enlarging tiny numbers to big so we can see...
int drawy=(int)(ny*100.0 + 300);  // ...the results properly. Plus centering to middle.

plot(drawx, drawy);
}

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?
« Last Edit: March 28, 2008, 04:06:26 AM by twinbee » Logged
juharkonen
Fractal Freshman
**
Posts: 7


View Profile
« Reply #1 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.
Logged
GFWorld
Fractal Fanatic
****
Posts: 252



View Profile WWW
« Reply #2 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  Smiley
***
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
Logged
Trifox
Administrator
Fractal Molossus
*****
Posts: 593


Frascinating!


View Profile WWW
« Reply #3 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 ?
Logged

---

divide and conquer - iterate and rule
fractalmovies.com
lycium
Fractal Bachius
*
Posts: 523



View Profile WWW
« Reply #4 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.
Logged

Pages: [1]
  Print  

 
Jump to:  


Related Topics
Subject Started by Replies Views Last post
Croco-Mandelbrot Best Fractal Animation eNZedBlue 0 201 Last post November 30, 2006, 10:12:40 PM
by eNZedBlue
3D Mandelbrot Movies Showcase (Rate My Movie) David Makin 0 214 Last post December 09, 2006, 11:38:14 PM
by David Makin
Why does the Mandelbrot set work? Mandelbrot & Julia Set Warp 5 312 Last post May 15, 2007, 10:39:17 PM
by FractalMonster
Twisted Mandelbrot Images Showcase (Rate My Fractal) doncasteel8587 6 246 Last post June 18, 2007, 04:52:33 AM
by doncasteel8587
Mandelbrot 3d Mutatorkammer Gallery Trifox 2 150 Last post March 19, 2008, 05:45:40 PM
by GFWorld

Powered by MySQL Powered by PHP Powered by SMF 1.1.7 | SMF © 2006-2008, Simple Machines LLC

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.428 seconds with 27 queries. (Pretty URLs adds 0.038s, 2q)