Finite orbit constellations in C

/* Arithmos: quadratic-orbit-basin
 * Compile: cc -std=c11 -O2 quadratic-orbit-basin.c -lm -o quadratic-orbit-basin
 * Run:     ./quadratic-orbit-basin
 * Output:  quadratic-orbit-basin.svg (open this file in a browser)
 * Optional output path: ./quadratic-orbit-basin 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;}

/* Finite functional graph; radius records steps before entering a cycle. */
static void draw(void) {
    const int modulus=97,constant=1; /* Editable positive modulus, constant. */
    int *seen=malloc((size_t)modulus*sizeof *seen);
    int *path=malloc((size_t)modulus*sizeof *path);
    int *depth=calloc((size_t)modulus,sizeof *depth);
    int *cycle=calloc((size_t)modulus,sizeof *cycle);
    if(!seen||!path||!depth||!cycle){free(seen);free(path);free(depth);free(cycle);return;}
    int maxdepth=0;
    for(int k=0;k<modulus;++k){
        for(int j=0;j<modulus;++j)seen[j]=-1;
        int x=k,length=0;
        while(seen[x]<0){
            seen[x]=length;path[length++]=x;
            x=(x*x+constant)%modulus;if(x<0)x+=modulus;
        }
        depth[k]=seen[x];cycle[k]=path[seen[x]];
        for(int j=seen[x];j<length;++j)if(path[j]<cycle[k])cycle[k]=path[j];
        if(depth[k]>maxdepth)maxdepth=depth[k];
    }
    double unit=282/(1+.16*maxdepth);
    for(int k=0;k<modulus;++k){
        int j=(k*k+constant)%modulus;if(j<0)j+=modulus;
        double a=2*NT_PI*k/modulus-NT_PI/2,b=2*NT_PI*j/modulus-NT_PI/2;
        double r=unit*(1+.16*depth[k]),s=unit*(1+.16*depth[j]);
        nt_line(500+r*cos(a),345-r*sin(a),500+s*cos(b),345-s*sin(b),
            (double)cycle[k]/modulus,.6,1.15);
    }
    for(int k=0;k<modulus;++k){
        double a=2*NT_PI*k/modulus-NT_PI/2,r=unit*(1+.16*depth[k]);
        nt_dot(500+r*cos(a),345-r*sin(a),2.6,(double)cycle[k]/modulus,1);
    }
    nt_text(45,675,"Quadratic modular map. Radius: tail length. Color: eventual cycle identity.");
    free(seen);free(path);free(depth);free(cycle);
}

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] : "quadratic-orbit-basin.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;
}