Collatz branches in C

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

/* Only trajectories reaching 1 within CAP are rendered. Unsigned overflow is
   checked before 3n+1. Finite examples do not prove the Collatz conjecture. */
static int nt_collatz_chain(uint64_t start,uint64_t *chain,int cap) {
    int n=0;uint64_t value=start;
    while(n<cap) {
        chain[n++]=value;if(value==1)return n;
        if(value&1U) {
            if(value>(UINT64_MAX-1)/3)return 0;
            value=3*value+1;
        } else value/=2;
    }
    return 0;
}
static void draw(void) {
    enum { STARTS=300, CAP=2000 };
    const double TURN=11.0*NT_PI/180.0; /* Editable turn angle, in degrees. */
    uint64_t chain[CAP];
    double xmin=0,xmax=0,ymin=0,ymax=0,scale=1,mx=0,my=0;
    /* First pass fits every path; second pass draws the same exact rules. */
    for(int pass=0;pass<2;++pass) {
        if(pass){scale=fmin(900/fmax(1,xmax-xmin),580/fmax(1,ymax-ymin));
            mx=.5*(xmin+xmax);my=.5*(ymin+ymax);}
        for(int start=2;start<=STARTS;++start) {
            int count=nt_collatz_chain((uint64_t)start,chain,CAP);
            if(!count)continue;
            double x=0,y=0,heading=-NT_PI/2;
            char color[8];nt_color(start/(double)STARTS,color);
            if(pass)fprintf(nt_out,"<path d=\"M%.3f %.3f",500-mx*scale,340-my*scale);
            /* Reverse the trajectory from 1; predecessor parity bends it. */
            for(int j=count-2;j>=0;--j) {
                heading+=(chain[j]&1U)?-TURN:TURN;
                x+=cos(heading);y+=sin(heading);
                if(!pass) {
                    if(x<xmin)xmin=x;if(x>xmax)xmax=x;
                    if(y<ymin)ymin=y;if(y>ymax)ymax=y;
                } else fprintf(nt_out," L%.3f %.3f",500+(x-mx)*scale,340+(y-my)*scale);
            }
            if(pass)fprintf(nt_out,"\" fill=\"none\" stroke=\"%s\" stroke-opacity=\"0.18\" stroke-width=\"1.15\"/>\n",color);
        }
    }
    nt_text(50,675,"Collatz: reverse finite trajectories; parity supplies each bend");
}

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] : "collatz.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;
}