Fun fact!

Linum’s logo is defined by the following double inequality:

\frac{1-\left|\cos\left(\frac{5}{2}\theta\right)\right|}{4}\le r\le\left|\cos\left(\frac{5}{2}\theta\right)\right|^\frac{1}{8}

And it can be rendered using the C code and command below:

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <math.h>

#define SIZE 4096

double map(double val) {
    return 2 * (val / (SIZE - 1)) - 1;
}

uint8_t lerp(double c, double t) {
    return UCHAR_MAX * ((1 - t) + t * c);
}

uint32_t color(double t) {
    uint32_t r, g, b;

    t = sqrt(t);
    r = lerp(0.25, t);
    g = lerp(0.50, t);
    b = lerp(0.75, t);

    return (b << 24) | (g << 16) | (r << 8) | UCHAR_MAX;
}

int main(void) {
    FILE *file = fopen("out.raw", "wb");
    size_t size = 4 * SIZE * SIZE;
    uint32_t *buffer = malloc(size);
    double x, y, t, r;
    int i;

    if (file == NULL)
        return EXIT_FAILURE;

    for (size_t row = 0; row < SIZE; row++) {
        for (size_t col = 0; col < SIZE; col++) {
            x = map(col);
            y = map(row);
            t = atan2(y, x);
            r = sqrt(x * x + y * y);
            i = SIZE * row + col;

            if (r >= 0.25 * (1 - fabs(cos(2.5 * t))) &&
                r <= pow(fabs(cos(2.5 * t)), 0.125))
                buffer[i] = color(r);

            else buffer[i] = 0;
        }
    }
    fwrite(buffer, 4, size, file);
    fclose(file);

    return EXIT_SUCCESS;
}

ffmpeg -pix_fmt argb -s 4096x4096 -i out.raw -vframes 1 out.png