improper mandelbrot set output plotting - algorithm

Question

i am trying to write a code to display Mandelbrot set for the numbers between
(-3,-3) to (2,2) on my terminal.
The main function generates & feeds a complex number to analyze function.
The analyze function returns character "*" for the complex number Z within the set and "." for the numbers which lie outside the set.
The code:
#define MAX_A 2 // upperbound on real
#define MAX_B 2 // upper bound on imaginary
#define MIN_A -3 // lowerbnd on real
#define MIN_B -3 // lower bound on imaginary
#define NX 300 // no. of points along x
#define NY 200 // no. of points along y
#define max_its 50
int analyze(double real,double imag);
void main()
{
double a,b;
int x,x_arr,y,y_arr;
int array[NX][NY];
int res;
for(y=NY-1,x_arr=0;y>=0;y--,x_arr++)
{
for(x=0,y_arr++;x<=NX-1;x++,y_arr++)
{
a= MIN_A+ ( x/( (double)NX-1)*(MAX_A-MIN_A) );
b= MIN_B+ ( y/( (double)NY-1 )*(MAX_B-MIN_B) );
//printf("%f+i%f ",a,b);
res=analyze(a,b);
if(res>49)
array[x][y]=42;
else
array[x][y]=46;
}
// printf("\n");
}
for(y=0;y<NY;y++)
{
for(x=0;x<NX;x++)
printf("%2c",array[x][y]);
printf("\n");
}
}
The analyze function accepts the coordinate on imaginary plane ;
and computes (Z^2)+Z 50 times ; and while computing if the complex number explodes, then function returns immidiately else the function returns after finishing 50 iterations;
int analyze(double real,double imag)
{
int iter=0;
double r=4.0;
while(iter<50)
{
if ( r < ( (real*real) + (imag*imag) ) )
{
return iter;
}
real= ( (real*real) - (imag*imag) + real);
imag= ( (2*real*imag)+ imag);
iter++;
}
return iter;
}
So, i am analyzing 60000 (NX * NY) numbers & displaying it on the terminal
considering 3:2 ratio (300,200) , i even tried 4:3 (NX:NY) , but the output remains same and the generated shape is not even close to the mandlebrot set :
hence, the output appears inverted ,
i browsed & came across lines like:
(x - 400) / ZOOM;
(y - 300) / ZOOM;
on many mandelbrot codes , but i am unable to understand how this line may rectify my output.
i guess i am having trouble in mapping output to the terminal!
(LB_Real,UB_Imag) --- (UB_Real,UB_Imag)
| |
(LB_Real,LB_Imag) --- (UB_Real,LB_Imag)
Any Hint/help will be very useful

Answer 1

The Mandelbrot recurrence is zn+1 = zn2 + c.
Here's your implementation:
real= ( (real*real) - (imag*imag) + real);
imag= ( (2*real*imag)+ imag);
Problem 1. You're updating real to its next value before you've used the old value to compute the new imag.
Problem 2. Assuming you fix problem 1, you're computing zn+1 = zn2 + zn.
Here's how I'd do it using double:
int analyze(double cr, double ci) {
double zr = 0, zi = 0;
int r;
for (r = 0; (r < 50) && (zr*zr + zi*zi < 4.0); ++r) {
double zr1 = zr*zr - zi*zi + cr;
double zi1 = 2 * zr * zi + ci;
zr = zr1;
zi = zi1;
}
return r;
}
But it's easier to understand if you use the standard C99 support for complex numbers:
#include <complex.h>
int analyze(double cr, double ci) {
double complex c = cr + ci * I;
double complex z = 0;
int r;
for (r = 0; (r < 50) && (cabs(z) < 2); ++r) {
z = z * z + c;
}
return r;
}