spirals - Ulam's spiral

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.

Code:

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

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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:

Code:

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#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;
}

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attached is the .exe file in a zip container

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

Code:

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#define ZERO 239

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=).

Z.

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 :D)

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

Z.

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

I Did =). Pretty nifty.

Z.

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

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.

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