The Computer Graphics Companion Online Edition Damian Scattergood 1999-2001
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FRACTALS

THE MANDELBROT SET

Basic Mandelbrot Set Algorithm

// Mandelbrot Set Drawing Routine.
void Mandelbrot ( )
{
int maxcol = 160; //Maximum number of pixel columns to display
int maxrow = 100; //Maximium number of pixel rows to display.
int max_colors = 255; //Maximum colors to display
int max_it = 256; //Maximum number of iterations.
int max_size =4;
float PMAX=1.75, PMIN=-1.75, QMAX=1.5, QMIN=-1.5;
float P,DP,DQ,X,Y,XS,YS;
int color, row,col;

DP=(PMAX-PMIN)/(maxcol-1);
DQ=(QMAX-QMIN)/(maxrow-1);
for (col=0; col<=maxcol; col++) {
P=PMIN + col*DP;
for (row=0; row<=maxrow; row++) {
X=Y=0.0;
for (color=0; color<=max_it; color++) {
XS=X*X;
YS=Y*Y;
if ((XS+YS) > max_size) break;
Y=2*X*Y+(QMIN+row*DQ);
X=XS-YS+P;
}

_setcolor(color % max_colors);
_setpixel(col,row);
}
}
}

THE ROSE

By plotting certain functions set graphic images can be created.
Sketch the rose r = a cos3A
Sketch the rose r = a sin 5A

r = ra Cos (3A) Rose ( 100, 100, 3 , 50);	r = ra Cos (5A) Rose (100, 100, 5, 50);

//
//Rose()
//
// Draws the Rose diagram of the equation -
// r = ra*cos (n*A);
//Draw a rose equation-
//Paramters - xc,yc : Center of Rose.
// - n : Cos Multiplication Number
// - ra ; Rose Radius.

#define PI 3.14
void Rose(xc,yc,n,ra)
double xc,yc; //centre of Rose
double n; //n value for Equation r = a*cos(n*A)
double ra; //True Rose Radius
{
int r;
double a;
double x,y;
double F=PI/180;
double xr;
double x1,y1;

//Calculate start point
r = 1;
a = (double) r * F;
xr = ra*cos (n*a); //Equation r=a*cos(N*A)
x1 = xc + xr*cos (a);
y1 = yc + xr*sin (a);
Moveto ( x1, y1); //Move to First Point.

//Draw Rose
for (r = 2; r < 360; r++) {
a = (double) r * F;
xr = ra*cos (n*a); //Equation r=a*cos(N*A)
x = xc + xr*cos (a);
y = yc + xr*sin (a);
Lineto (x, y); //Draw a line from first point to new point.
}
}

LISSAJOUS FIGURES

Lissajous figures are graphs of the parametric equations of

These are most usually found in the study of electricity.
By varying the input parameters to the above equation quite interesting results can be achieved.
Below are some examples.

Lissajous ( 200, 200, 20, 4, 7, 3, 11); x = 4 Sin 7t, y = 3 Cos 11t	lissajous ( 200, 200, 20, 3, 2, 3, 6); x = 3 Sin 2t, y = 3 Cos 6t

//
//Lissajous()
//
//Draw a Lissajous graph
//xc,yc = Centre of Lissajous Graph
//Sc = scale factor
//a,w1 = x values for x = a Sin w1 t
//b,W2 = y values for y = b Cos w2 t
//
void lissajous (xc, yc, Sc, a, w1, b, w2)
float xc, yc;
float Sc;
float a,b,w1,w2;
{
float PI = 3.14
float r;
float x,y;
for ( r = 1; r < 5 * PI; r += (PI / 360) ) {
x = xc + Sc * (a * Sin (w1 * r) );
y = yc + Sc * (b * Cos (w2 * r) );
Pixel (x, y);
}
}