spirals - Ulam's spiral

[jim mcnamara]

about 15 years ago, I wrote this code which draws Ulam's spiral.

If you start with one, put a series of numbers in a counter-clockwise spiral around it, then highlight the numbers that are prime, you get an interesting effect - prime numbers appear as 'lines'. Nobody can explain it.

     10  . . . .
      9 2 3   .
      8 1 4   .
      7 6 5   . 
    .   .   .    .

Anyway, as a sort-of followup to the sprial discussion attached is the Turbo C code (V 2.0) to make the spiral. It ran on my XP box under the command prompt. Amazing....

Here is the code:

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <graphics.h>
#include <conio.h>
#include <time.h>
#include <dos.h>
#define ZERO 239
#define MAX_PT 479
typedef struct XYcoord{
      int x;
      int y;
};
static struct XYcoord XY;


void display_spiral(FILE *);
void init_graph(void);
void plot(int);
void wait(void);
void iterate(FILE *);

unsigned long toint(double);
double todbl(unsigned long);
void test(FILE *);
void calc_primes(FILE *);
void add(unsigned long,FILE *in);
static unsigned long counter=0;
static unsigned long base_list[201];

static unsigned long active_base=0;
static const unsigned base_max=200;
static unsigned long prime;

int main(void){
        FILE *out;
	test(out=fopen("prime.txt","wb+"));
	calc_primes(out);
	fflush(out);
        display_spiral(out);
	fclose(out);
	return 0;
}
void calc_primes(FILE *out){
	register unsigned long i,j,k;
	unsigned long max;
	prime=1;
	add(1,out);
        base_list[0]=2;
	add(2,out);
        base_list[1]=3;
	add(3,out);
	prime=0;
	add(4,out);
	prime=1;
        base_list[2]=5;
	add(5,out);
        active_base=2;
	max=479;
	max*=479;
	for (i=6;counter<max;i++,counter++){
	     if(!i%2){
             	prime=0;
             	add(i,out);
             	continue;
             }
             k=toint(sqrt(todbl(i)))+1;
             prime=1;
	     for(j=0;j<=active_base && prime ;j++){
		   if(i%base_list[j]==0) prime=0;}
             j=base_list[active_base]+2;
	     for(;j<=k && prime;j+=2) {
		   if(i%j==0) prime=0; }
             add(i,out);
	}
	printf("processed numbers=%ld\n",counter);
	return;
}
unsigned long toint(double z){
     char tmp[20];
     sprintf(tmp,"%.0f",z);
     return atol(tmp);
}

void test(FILE *tst){
    if(tst==NULL){
      perror("Error opening file");
      exit(EXIT_FAILURE);
      return;
      }
}
void add(unsigned long i, FILE *out){

      char output=0x00;
      if(prime){

         if(active_base < base_max){
         	  active_base++;
	          base_list[active_base]=i;
         }
      }
      if(prime==1) output=0x01;
      if(prime==0) output=0x00;
      fprintf(out,"%c",output);
      return;
}
double todbl(unsigned long i){
	char tmp[20];
	sprintf(tmp,"%lu",i);
        return atof(tmp);
}
void display_spiral(FILE *src){
	char output;
	int i;

    	fseek(src,0L,SEEK_SET);
    	init_graph();
    	XY.x=ZERO;
    	XY.y=ZERO;
	plot(1);
	fread(&output,1,1,src);
	iterate(src);
        wait();
        return;
}
void iterate(FILE *src){
	int i;
	int ok=1;
	char output;
        int currentwidth=0;
        int currentheight=0;
        while(ok){
             currentwidth++;
	     currentheight++;
	     for(i=currentwidth;i&&ok;i--){
             	ok=fread(&output,1,1,src);
             	if(ok) {
             	     XY.x+=1;
             	     plot(output);
             	}
	     }

	     for(i=currentheight;i&&ok;i--){
             	ok=fread(&output,1,1,src);
             	if(ok) {
             	     XY.y+=1;
             	     plot(output);
             	}
             }
             currentwidth++;
	     for(i=currentwidth;i&&ok;i--){
             	ok=fread(&output,1,1,src);
             	if(ok) {
             	     XY.x-=1;
             	     plot(output);
             	}
             }
             currentheight++;
             for(i=currentheight;i&&ok;i--){
             	ok=fread(&output,1,1,src);
             	if(ok) {
             	     XY.y-=1;
             	     plot(output);
             	}

	     }
	}
}

void wait(void){
	char ch;
        settextstyle(TRIPLEX_FONT,HORIZ_DIR,0);
        setcolor(YELLOW);
        outtextxy(10,430,"ESC = Quit");
  	while(1){
  		ch = getche();
  		if (ch == 27) {
  	 		closegraph();
  	 		break;
  	 	}
  	 	delay(100);
  	}
  	cleardevice();
}


void plot(int color){
	if(!color)return;
	if(XY.x && XY.y )
	             	putpixel(XY.x,XY.y,color+14);
        return;
}

void init_graph(void){
	int g_driver,g_mode;
        struct viewporttype pt;
        detectgraph(&g_driver,&g_mode);
        initgraph(&g_driver,&g_mode,"c:\TC");
        setbkcolor(BLACK);
        getviewsettings(&pt);
        return;
}

[jim mcnamara]

attached is the .exe file in a zip container

[Zaei]

Mozilla doesnt seem to like attachments here... so i will grab it in a sec... but I thought this was funny =):

#define ZERO 239

=).

Z.

[parksie]

A quick Google found me this:

http://www.alpertron.com.ar/ULAM.HTM

I agree, spooky stuff! (PS: 15 years ago was when I first got my sticky little paws on a keyboard )

[Zaei]

Win2k doesnt like it, so I dont get to see it =(.

Z.

[jim mcnamara]

Try Parksie's link - it shows what the thing looks like.

[Zaei]

I Did =). Pretty nifty.

Z.

[CornedBee]

Z: I could download it with Mozilla and execute it with Win2k...

[Zaei]

Ah, just had to slice the .php off the end =).

My install of Win2k doesnt like older stuff... Like I cant run Warcraft 2 =(.

Z.

[CornedBee]

Mine doesn't like Diablo2. I can run it, but is SLOOOOOOW...