1 files changed, 55 insertions, 0 deletions
diff --git a/src/serial-fractals.c b/src/serial-fractals.c
new file mode 100644
index 0000000..c5b9c4e
--- /dev/null
+++ b/src/serial-fractals.c
@@ -0,0 +1,55 @@
+#include "fractals.h"
+/*
+ * Computes the number of iterations it takes for a point z0 to diverge
+ * if the return value is equal to max_iterations, the point lies within the mandelbrot set
+ * This is an implementation the escape algorithm
+ */
+size_t mandelbrot(const double complex z0, const size_t max_iterations) {
+  double complex z = z0;
+  size_t iteration = 0;
+
+  while (cabs(z) <= 2 && iteration < max_iterations) {
+    z = z * z + z0;
+    iteration++;
+  }
+  return iteration;
+}
+
+/*
+ * Computes the number of iterations it takes for a point z0 to diverge
+ * if the return value is equal to max_iterations, the point lies within the multibrot set
+ * This is implementation closely matches mandelbrot
+ * Note, only positive integer powers are supported
+ */
+size_t multibrot(const double complex z0, const size_t max_iterations, const uintmax_t d){
+    double complex z = z0;
+    double complex ztemp;
+    size_t iteration = 0;
+    while(cabs(z) <= 2 && iteration < max_iterations){
+        ztemp = z;
+        for(size_t i = 0; i < d; i ++){
+            ztemp *= ztemp;
+        }
+        z = ztemp + z0;
+        iteration++;
+    }
+    return iteration;
+}
+
+/*
+ * Computes ????? for a julia set
+ * implementation of https://en.wikipedia.org/wiki/Julia_set#Pseudocode
+ */
+size_t julia(const double R, const double complex z0, const double complex c, const size_t max_iterations){
+    //FIXME: I'm notsure if this is currently implemented correctly
+    if(R*R - R >= cabs(z0)) return 0;
+    double complex z = z0;
+
+    size_t iteration = 0;
+    while(cabs(z) < R && iteration < max_iterations){
+        z = z * z + c;
+        iteration++;
+    }
+    return iteration;
+}
+