Did the.

Makefile

@@ -1,4 +1,4 @@
-NAME = project-name
+NAME = candelbrot
 
 TARGET = $(NAME).out
 
@@ -12,7 +12,7 @@ TEST_OBJ_DIR = $(TEST_BUILD_DIR)/obj
 CC = clang
 LINK = clang
 CFLAGS = -Wall
-LDFLAGS =
+LDFLAGS = -lm -lSDL2
 
 SRC_FILES = $(wildcard $(SRC_DIR)/*.c)
 OBJ_FILES = $(patsubst $(SRC_DIR)/%.c, $(OBJ_DIR)/%.o, $(SRC_FILES))

src/include/main.h

@@ -1,2 +1,19 @@
-// This file serves no real purpose, except to appease my poorly-written
-// makefile :P.
+#ifndef MAIN_H
+#define MAIN_H
+
+#include <SDL2/SDL.h>
+
+#include <stdio.h>
+#include <complex.h>
+
+#define WIDTH 1920
+#define HEIGHT 1080
+#define MAX_I 1024
+
+// Number of iterations for a point on the set.
+int mandelbrot(double real, double imag);
+
+// Map pixel coords to complex plane.
+void render(SDL_Renderer* renderer, double zm, double dx, double dy);
+
+#endif

src/main.c

@@ -1,7 +1,78 @@
-#include <stdio.h>
+#include "include/main.h"
+
+int mandelbrot(double real, double imag) {
+    double complex z = 0;
+    double complex c = real + imag * I;
+    int i = 0;
+
+    while (cabs(z) <= 2.0 && i < MAX_I) {
+        z = z * z + c;
+        i++;
+    }
+
+    return i;
+}
+
+void render(SDL_Renderer *renderer, double zm, double dx, double dy) {
+    for (int x = 0; x < WIDTH; x++) {
+        for (int y = 0; y < HEIGHT; y++) {
+            double real = (x - WIDTH / 2.0) * zm + dx;
+            double imag = (y - HEIGHT / 2.0) * zm + dy;
+
+            int i = mandelbrot(real, imag);
+
+            int col = (i == MAX_I) ? 0 : (255 * i / MAX_I);
+            SDL_SetRenderDrawColor(renderer, col, col, col, 255);
+            SDL_RenderDrawPoint(renderer, x, y);
+        }
+    }
+}
 
 int main(int argc, char** argv) {
-    printf("Hello, world!\n");
+    if (SDL_Init(SDL_INIT_VIDEO) != 0) {
+        printf("SDL_Init Error: %s\n", SDL_GetError());
+        return 1;
+    }
+
+    SDL_Window *win = SDL_CreateWindow("Mandelbrot Set", 100, 100, WIDTH, HEIGHT, SDL_WINDOW_SHOWN | SDL_WINDOW_BORDERLESS);
+    if (win == NULL) {
+        printf("SDL_CreateWindow Error: %s\n", SDL_GetError());
+        SDL_Quit();
+        return 1;
+    }
+
+    SDL_Renderer *renderer = SDL_CreateRenderer(win, -1, SDL_RENDERER_ACCELERATED | SDL_RENDERER_PRESENTVSYNC);
+    if (renderer == NULL) {
+        SDL_DestroyWindow(win);
+        printf("SDL_CreateRenderer Error: %s\n", SDL_GetError());
+        SDL_Quit();
+        return 1;
+    }
+
+    double zoom = 4.0 / WIDTH;
+    double offsetX = -0.7;   // Center point in the Mandelbrot set
+    double offsetY = 0.0;
+
+    int quit = 0;
+    while (!quit) {
+        SDL_Event e;
+        while (SDL_PollEvent(&e)) {
+            if (e.type == SDL_QUIT) {
+                quit = 1;
+            }
+        }
+
+        SDL_SetRenderDrawColor(renderer, 0, 0, 0, 255);
+        SDL_RenderClear(renderer);
+
+        render(renderer, zoom, offsetX, offsetY);
+
+        SDL_RenderPresent(renderer);
+    }
+
+    SDL_DestroyRenderer(renderer);
+    SDL_DestroyWindow(win);
+    SDL_Quit();
 
     return 0;
 }