hutch@sdcsvax.UUCP (Jim Hutchison) (07/08/85)
fractal()
For all of you folks out there with appetite for source,
I have posted a copy of several routines which can draw Koch
lakes, Gosper Curves, and a Monkey curve.
If you don't know what these are, they are self avoiding
curves well described in Benoit Mandelbrot's Book "The Fractal
Geometry of Nature". If nothing else look at the pretty
pictures ( Planet Rise!!! ).
# -- strip top and signature --
# This is a shell archive. Remove anything before this line,
# then unpack it by saving it in a file and typing "sh file".
#
# Wrapped by gryphon!hutch on Mon Jul 8 01:23:24 PDT 1985
# Contents: plot.c gosper.c koch.c monkey.c g.h gen.h README
echo x - plot.c
sed 's/^@//' > "plot.c" <<'@//E*O*F plot.c//'
/*
* Plot_line()
*
* Draw a line by length and angle relative to current x,y
*
* Author: Jim Hutchison (hutch@sdcsvax)
* (this is free, but credit me)
*/
#include <usercore.h>
#include <math.h>
#include "g.h"
/*
* Plot a line by length and angle from current position
*/
plot_line(length,angle)
double length,angle;
{
double dx,dy;
MOD(angle,TWOPI);
dx = length * cos(angle);
dy = length * sin(angle);
line_rel_2( dx, dy);
}
@//E*O*F plot.c//
chmod u=rw,g=r,o=r plot.c
echo x - gosper.c
sed 's/^@//' > "gosper.c" <<'@//E*O*F gosper.c//'
/*
* Gosper()
*
* Draw a Gosper curve according to Dr. Mandelbrot.
* start with flip at 1 usually, but -1 is fine also.
*
* Author: Jim Hutchison (hutch@sdcsvax)
* (this is free, but credit me)
*/
#include <usercore.h>
#include <math.h>
#include "g.h"
#include "gen.h"
#ifdef GEN_SIDES
#undef GEN_SIDES
#endif
#define GEN_SIDES 7
#define GEN_MAX GEN_SIDES - 1L
static GEN generator[GEN_SIDES] = {
/* angle flip */
{ 0.0, 1 },
{ PIO3, -1 },
{ PI, -1 },
{ (2.0 * PIO3), 1 },
{ 0.0, 1 },
{ 0.0, 1 },
{ (TWOPI - PIO3), -1 }
};
gosper(len,angle,min_len,flip)
double len,angle,min_len;
int flip;
{
register int i;
register GEN *gp;
if (len > min_len) { /* draw generator */
angle += (TWOPI - PIO6);/* tilt */
gp = &generator[ (flip == 1)? 0 : GEN_MAX ];
for(i = 0 ; i < GEN_SIDES ; i++, gp += flip)
gosper(len/2.0, angle + gp->angle, min_len, gp->flip * flip);
}
else /* draw side */
plot_line(len, angle);
}
@//E*O*F gosper.c//
chmod u=rw,g=r,o=r gosper.c
echo x - koch.c
sed 's/^@//' > "koch.c" <<'@//E*O*F koch.c//'
/*
* koch()
*
* Draw a Koch lake according to Dr. Mandelbrot.
*
* Author: Jim Hutchison (hutch@sdcsvax)
* (this is free, but credit me)
*/
#include <usercore.h>
#include <math.h>
#include "g.h"
#include "gen.h"
koch(len,angle,min_len)
double len,angle,min_len;
{
int i;
for (i = 0 ; i < 4 ; i++, angle += PIO2) /* square seed */
koch_side(len, angle, min_len);
}
#ifdef GEN_SIDES
#undef GEN_SIDES
#endif
#define GEN_SIDES 8
GEN genkoch[GEN_SIDES] = {
/* Angle */
{ 0.0 },
{ PIO2 },
{ 0.0 },
{ - PIO2 },
{ - PIO2 },
{ 0.0 },
{ PIO2 },
{ 0.0 }
};
/*
* Draw a side recursively.
*/
koch_side(len,angle,min_len)
double len,angle,min_len;
{
register int i;
GEN *gp;
if (len > min_len) /* draw generator */
for(i = 0, gp = genkoch ; i < GEN_SIDES ; i++, gp++)
koch_side(len/2.0, angle + gp->angle, min_len);
else /* draw side */
plot_line(len, angle);
}
@//E*O*F koch.c//
chmod u=rw,g=r,o=r koch.c
echo x - monkey.c
sed 's/^@//' > "monkey.c" <<'@//E*O*F monkey.c//'
/*
* Monkey()
*
* Draw a Monkey curve according to Dr. Mandelbrot.
*
* Author: Jim Hutchison (hutch@sdcsvax)
* (this is free, but credit me)
*/
#include <usercore.h>
#include <math.h>
#include "g.h"
#include "gen.h"
#ifdef GEN_SIDES
#undef GEN_SIDES
#endif
#define GEN_SIDES 11
#define GEN_MAX GEN_SIDES - 1
GEN genmonkey[GEN_SIDES] = {
/* Angle Flip Scale */
{ PIO3, -1, 1.0 }, /* R */
{ PIO3, 1, 1.0 }, /* L */
{ 0.0, 1, 1.0 }, /* L */
{ (TWOPI - PIO3), 1, 1.0 }, /* L */
{ (2.0 * PIO3 + PIO6), 1, 0.5 }, /* L */
{ (2.0 * PIO3 + PIO6), -1, 0.5 }, /* R */
{ (PI + PIO6), -1, 0.5 }, /* R */
{ (TWOPI - PIO2), -1, 0.5 }, /* R */
{ (TWOPI - PIO2), 1, 0.5 }, /* L */
{ 0.0, -1, 1.0 }, /* R */
{ 0.0, 1, 1.0 } /* L */
};
/*
* Draw a monkey curve
*/
monkey(len,angle,min_len,scale,flip)
double len,angle,min_len,scale;
int flip;
{
register int i;
GEN *gp;
if (len > min_len) { /* draw generator */
gp = &genmonkey[ (flip == 1)? 0 : GEN_MAX ];
for(i = 0 ; i < GEN_SIDES ; i++, gp += flip)
monkey(len/2.0,
angle + gp->angle,
min_len,
scale * gp->scale,
gp->flip * flip);
} else /* draw side */
plot_line(len * scale, angle);
}
@//E*O*F monkey.c//
chmod u=rw,g=r,o=r monkey.c
echo x - g.h
sed 's/^@//' > "g.h" <<'@//E*O*F g.h//'
/*
* G.h
*
* Constants for convenience when doing radial fractal work under SUNCORE
*
* Author: Jim Hutchison (hutch@sdcsvax)
*/
#define SQRT2 1.41421
#define PI 3.1415926536
#define PIO2 (PI / 2.0)
#define PIO3 (PI / 3.0)
#define PIO4 (PI / 4.0)
#define PIO6 (PI / 6.0)
#define TWOPIO3 (2.0 * PI / 3.0)
#define TWOPI (2.0 * PI)
#define MOD(a,b) while(a > b) a -= b /* sad but true */
@//E*O*F g.h//
chmod u=rw,g=r,o=r g.h
echo x - gen.h
sed 's/^@//' > "gen.h" <<'@//E*O*F gen.h//'
/*
* Author: Jim Hutchison (hutch@sdcsvax)
* Curve generators and initiators ( can be same structure )
* Various and sundry generators and a very general one.
*/
typedef struct gen { /* an initiator or generator */
double angle; /* next turtle turn */
int flip; /* Flip flop multiplier */
double scale; /* scale factor for sides */
double div; /* division factor for length */
} GEN;
@//E*O*F gen.h//
chmod u=rw,g=r,o=r gen.h
echo x - README
sed 's/^@//' > "README" <<'@//E*O*F README//'
These files:
g.ha few constants
gen.h generator structure
general.c a general curve generator
gosper.c gosper curve generator
koch.c koch curve generator
monkey.c monkey curve generator (My favorite)
plot.c plot a line relatively
Comprise a collection of simple fractal curve generators.
They do not generate nifty 3D dragons or towers or archs,
but they are entertaining and probably good for tiling.
All I ask is that you not (how incredibly unlikely) try
to sell these for profit. I can ofcourse assume no respon-
sibility for how these work out for you. They work fine for
me on a SUN (TM) workstation under 4.2 Unix (TM) using SUN-
core.
Jim Hutchison
hutch@sdcsvax
{ihnp4,ucbvax}!sdcsvax!hutch
@//E*O*F README//
chmod u=rw,g=r,o=r README
exit 0
--
/*
Jim Hutchison UUCP: {dcdwest,ucbvax}!sdcsvax!hutch
ARPA: hutch@sdcsvax
< Ofcourse these statements are only mine, not my employers. >
*/