// THIS PROGRAM PLOTS THE MANDELBROT SET. A SUBSET OF THE COMPLEX PLANE IS

// DIVIDED UP IN TO AN NxN GRID, AND AN ITERATIVE EQUATION IS APPLIED TO EACH

// POINT ON THIS GRID. IF, AFTER A PREDETERMINED NUMBER OF ITERATIONS, THE

// OUTPUT NUMBER HAS NOT EXCEEDED A CERTAIN ABSOLUTE MAGNITUDE THEN THE POINT

// IS PLOTTED. OTHERWISE IT IS NOT PLOTTED.

// AUTHOR: LACHLAN STONEY

//CONSTANTS:

//MNI = Max # of iterations

//N = # of subdivisions of the plotting window.

//R = Max absolute magnitude of iteration

//XMIN, YMIN, ... = boundaries of plotting window.

#define MNI 500

#define N 1000

#define R 3

#define XMIN -1.5

#define XMAX 0.5

#define YMIN -1.0

#define YMAX 1.0

//Includes

#include <math.h>

#include <stdlib.h>

#include <stdio.h>

#include <cpgplot.h>

//The structure of a complex number is defined

struct cnum

};

//Declaration of Functions

void CPRINT(struct cnum c); // prints a complex number in coordinate form. (diagnostic tool)

struct cnum CPROD( struct cnum c1, struct cnum c2); // multiplies two complex numbers c1 and c2;

struct cnum CADD( struct cnum c1, struct cnum c2); // adds " " "

struct cnum FJULIA( struct cnum c1 ); // iterative function for Julia Set

struct cnum FMANDEL( struct cnum z, struct cnum c ); // iteractive function for Mandelbrot Set

//Main program

void main()

{

float RES = (XMAX - XMIN)/N; //resolution

int i,j,p;

//************************* PGPLOT CODE ***************************

cpgbeg(0,"?",1,1);

cpgpage();

cpgsci(1); // axis color

cpgpap(0,1);

//axis limits

cpgswin(XMIN,XMAX,YMIN,YMAX);

cpgbox("BCN",1, 0, "BCN", 1, 0); // draw the axes

cpgsci(1); //data color

cpgsch(0.00000000000001); //data point size

//******************* GRID ALGORITHM AND PLOTTING ********************

struct cnum z; // z = (0,0) = initial number

struct cnum c; // c is a complex variable

z.cx = 0;

z.cy = 0;

for(i=0;i<N;i++) //look at every point on grid

{

for(j=0;j<N;j++)

{

c.cx = XMIN + i*RES; //assign c = current point

c.cy = YMIN + j*RES;

CPRINT(c);

for(p=0;p<MNI;p++) //apply MNI iterations to z

{ //using c = current point

z = FMANDEL(z,c);

if ( z.cx*z.cx + z.cy*z.cy > R) // if iteration "blows up"...

{

z.cx = 0;

z.cy = 0; //stay at z=c=0

c.cx = 0;

c.cy = 0;

}

} //end of interation. z = final number

if (z.cx*z.cx + z.cy*z.cy < R) //if iteration hasn't blown up...

{

float X[1], Y[1];

X[0] = c.cx;

Y[0] = c.cy;

cpgpt(1,X,Y,17); // plot point c

}

}

}

printf("\n\n");

cpgend();

}

//FUNCTIONS

//Iterative equation for the Mandelbrot Set

struct cnum FMANDEL( struct cnum z, struct cnum c)

{

struct cnum value;

value = CPROD(z,z);

value = CADD(value,c); // z = z^2 + c

return value;

}

// Iterative equation for Julia Set

struct cnum FJULIA( struct cnum c1 )

{

struct cnum C; //define constant C

C.cx = 0.0;

C.cy = 1.0;

struct cnum value;

value = CPROD(c1,c1);

value = CADD(value,C);

return value;

}

// Addition function

struct cnum CADD( struct cnum c1, struct cnum c2)

{

double a = c1.cx;

double b = c1.cy;

double c = c2.cx;

double d = c2.cy;

struct cnum sum;

sum.cx = a+c;

sum.cy = b+d;

return sum;

}

// Multiplication function

struct cnum CPROD( struct cnum c1, struct cnum c2)

{

double a = c1.cx;

double b = c1.cy;

double c = c2.cx;

double d = c2.cy;

struct cnum product;

product.cx = a*c - b*d;

product.cy = a*d + b*c;

return product;

}

// print function

void CPRINT(struct cnum c)

{

double cx = c.cx;

double cy = c.cy;

printf("\n( %0.3f , %0.3f )",cx,cy);

}