From 625d99871e5d18e0aa54a95cfce2fa37e46b4095 Mon Sep 17 00:00:00 2001
From: JP Appel <jeanpierre.appel01@gmail.com>
Date: Fri, 19 Apr 2024 22:29:11 -0400
Subject: implemented multibrot and mandelbrot serial pixel functions

---
 src/mandelbrot.c | 52 ++++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 50 insertions(+), 2 deletions(-)

diff --git a/src/mandelbrot.c b/src/mandelbrot.c
index 094ea0e..63db30d 100644
--- a/src/mandelbrot.c
+++ b/src/mandelbrot.c
@@ -1,3 +1,51 @@
-int main(const int argc, const char* argv[]){
-    return 0;
+#include <complex.h>
+#include <stddef.h>
+#include <stdint.h>
+#include <stdio.h>
+
+#include "plotting.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 esacpe algorithm
+ */
+size_t mandelbrot(double complex z0, size_t max_iterations) {
+  double complex z = 0.0 + 0.0*I;
+  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(double complex z0, size_t max_iterations, uintmax_t d){
+    double complex z = 0.0 + 0.0*I;
+    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;
+}
+
+
+int main(const int argc, const char *argv[]) {
+    double complex z = 1.0 + 0.0*I;
+    size_t result = mandelbrot(z, 1000);
+    printf("Input: %f+%fI\n", creal(z), cimag(z));
+    printf("result: %zu\n", result);
 }
-- 
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