arithmos
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Times-table circle in C

A complete program. Standard C, a compiler, and the rule behind the shape.

Output generated by this C program: Times-table circle
Generated by the C program below Download image ↗
FROM SOURCE TO SHAPE

Run it in three steps.

  1. Save the source.

    Download times.c into a folder on your computer.

  2. Compile it.

    In that folder, run this with GCC or Clang:

    cc -std=c11 -O2 times.c -lm -o times
  3. Make the image.
    ./times

    Open times.svg in a browser to see the result.

On Windows with GCC, name the executable times.exe and run it from the same folder.

THE RULE IN THE PROGRAM

How the picture is built

Place N equally spaced nodes on a circle. Connect node k to angular position (k×MULTIPLIER) modulo N. For integer multiplier 2, the dense family of chords has a cardioid envelope.

Make it your own

N=360 nodes; MULTIPLIER=2.0; RADIUS=285. Try integer multipliers 3, 4, and 5 for other envelopes.

With a noninteger multiplier, an endpoint can fall between marked nodes. The code draws finitely many chords; their envelope is a limiting curve rather than an extra curve computed by the program. Each run produces one image; use Graphic mode for the interactive animation.

The complete source

times.c · 98 lines · no graphics libraries
Download .c ↓
/* Arithmos: times
 * Compile: cc -std=c11 -O2 times.c -lm -o times
 * Run:     ./times
 * Output:  times.svg (open this file in a browser)
 * Optional output path: ./times my-image.svg
 * Edit the constants in draw() to explore another case.
 */
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

static FILE *nt_out;
#define NT_PI 3.14159265358979323846

/* The small SVG writer keeps this program free of graphics dependencies.
 * Coordinates are pixels on a 1000 x 700 drawing surface.
 * t runs from 0 to 1 through mint, blue, rose, and gold.
 */
static inline void nt_color(double t, char hex[8]) {
    const double stops[4][3] = {
        {91,227,201}, {128,146,240}, {218,138,220}, {244,200,127}
    };
    t = fmax(0.0, fmin(1.0,t)) * 3.0;
    int band = (int)fmin(2.0,floor(t));
    double blend = t - band;
    int r[3];
    for (int k=0;k<3;k++) r[k]=(int)lround(stops[band][k]*(1.0-blend)+stops[band+1][k]*blend);
    snprintf(hex,8,"#%02x%02x%02x",r[0],r[1],r[2]);
}
static inline void nt_line(double x,double y,double X,double Y,double t,double alpha,double width) {
    char color[8];nt_color(t,color);
    fprintf(nt_out,"<path d=\"M%.3f %.3f L%.3f %.3f\" fill=\"none\" stroke=\"%s\" stroke-opacity=\"%.3f\" stroke-width=\"%.3f\"/>\n",x,y,X,Y,color,alpha,width);
}
static inline void nt_dot(double x,double y,double r,double t,double alpha) {
    char color[8];nt_color(t,color);
    fprintf(nt_out,"<circle cx=\"%.3f\" cy=\"%.3f\" r=\"%.3f\" fill=\"%s\" fill-opacity=\"%.3f\"/>\n",x,y,r,color,alpha);
}
static inline void nt_circle(double x,double y,double r,double t,double alpha,double width) {
    char color[8];nt_color(t,color);
    fprintf(nt_out,"<circle cx=\"%.3f\" cy=\"%.3f\" r=\"%.3f\" fill=\"none\" stroke=\"%s\" stroke-opacity=\"%.3f\" stroke-width=\"%.3f\"/>\n",x,y,r,color,alpha,width);
}
static inline void nt_rect(double x,double y,double w,double h,double t,double alpha) {
    char color[8];nt_color(t,color);
    fprintf(nt_out,"<rect x=\"%.3f\" y=\"%.3f\" width=\"%.3f\" height=\"%.3f\" fill=\"%s\" fill-opacity=\"%.3f\"/>\n",x,y,w,h,color,alpha);
}
static inline void nt_text(double x,double y,const char *text) {
    fprintf(nt_out,"<text x=\"%.3f\" y=\"%.3f\" fill=\"#ededf3\" font-family=\"monospace\" font-size=\"16\">",x,y);
    for (;*text;text++) {
        if (*text=='&') fputs("&amp;",nt_out);
        else if (*text=='<') fputs("&lt;",nt_out);
        else if (*text=='>') fputs("&gt;",nt_out);
        else fputc(*text,nt_out);
    }
    fputs("</text>\n",nt_out);
}
static inline int nt_gcd(int a,int b) {a=abs(a);b=abs(b);while(b){int r=a%b;a=b;b=r;}return a;}
static inline int nt_prime(int n) {if(n<2)return 0;for(int d=2;d<=n/d;d++)if(n%d==0)return 0;return 1;}

/* Multiplication modulo N on a circle. Edit MULTIPLIER: 2,3,4 create
   different chord envelopes; fractional values interpolate the mapping. */
static void draw(void) {
    const int N=360;const double MULTIPLIER=2.0,RADIUS=285;
    nt_circle(500,340,RADIUS,.2,.25,1);
    for(int k=0;k<N;++k) {
        double a=2*NT_PI*k/N-NT_PI/2;
        double target=fmod(k*MULTIPLIER,N);if(target<0)target+=N;
        double b=2*NT_PI*target/N-NT_PI/2;
        nt_line(500+RADIUS*cos(a),340+RADIUS*sin(a),
                500+RADIUS*cos(b),340+RADIUS*sin(b),k/(double)N,.32,.8);
    }
    for(int k=0;k<N;++k) {
        double a=2*NT_PI*k/N-NT_PI/2;
        nt_dot(500+RADIUS*cos(a),340+RADIUS*sin(a),1,k/(double)N,.9);
    }
    nt_text(50,675,"Connect k to multiplier times k, modulo the number of points.");
}

int main(int argc, char **argv) {
    if (argc > 2) {
        fprintf(stderr, "Usage: %s [OUTPUT.svg]\n", argv[0]);
        return EXIT_FAILURE;
    }
    const char *filename = argc == 2 ? argv[1] : "times.svg";
    nt_out = fopen(filename, "wb");
    if (!nt_out) { perror(filename); return EXIT_FAILURE; }
    fputs("<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"1000\" height=\"700\" viewBox=\"0 0 1000 700\">\n"
          "<rect width=\"1000\" height=\"700\" fill=\"#171721\"/>\n", nt_out);
    draw();
    fputs("</svg>\n", nt_out);
    int failed = ferror(nt_out);
    if (fclose(nt_out) != 0) failed = 1;
    if (failed) { fputs("Could not finish writing the image.\n", stderr); return EXIT_FAILURE; }
    printf("Wrote %s\n", filename);
    return EXIT_SUCCESS;
}
All 40 explorations, ready to compile.Download all C examples ↓