feat(c): simple complex numbers and divergence

mandelbrot.c

@@ -1,16 +1,44 @@
 #include "stdio.h"
+#include "math.h"
+
+#define MAX_DEPTH 50
 
 typedef struct {
   double real;
   double imag;
 } Complex;
 
-void complex_print(Complex z) {
+void cx_print(Complex z) {
   printf("%f + %f i", z.real, z.imag);
 }
 
+static inline Complex cx_square(Complex z) {
+  return (Complex){z.real * z.real - z.imag * z.imag, 2 * z.real * z.imag};
+}
+
+static inline Complex cx_add(Complex z1, Complex z2) {
+  return (Complex){z1.real + z2.real, z1.imag + z2.imag};
+}
+
+static inline double cx_abs(Complex z) {
+  return sqrt(z.real * z.real + z.imag * z.imag);
+}
+
+Complex f(Complex z, Complex c) {
+  return cx_add(cx_square(z), c);
+}
+
+// return iteration count, MAX_DEPTH if diverge
+int diverge(Complex c) {
+  int counter = 0;
+  Complex z = {0.0, 0.0};
+  for (z = f(z, c); cx_abs(z) < 2; counter++)
+    if (counter > MAX_DEPTH) return MAX_DEPTH;
+  return counter;
+}
+
 int main() {
   Complex z = {2.0, 4.0};
-  complex_print(z);
+  cx_print(z);
   return 1;
 }