diff --git a/Newton.py b/Newton.py
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+import math
+from PIL import Image
+
+width, height = 800, 800
+max_iter = 40
+tolerance = 0.001  # Wie nah müssen wir an der Nullstelle sein?
+
+# Die drei Nullstellen von z^3 - 1 = 0
+roots = [
+    complex(1, 0),
+    complex(-0.5, math.sqrt(3) / 2),
+    complex(-0.5, -math.sqrt(3) / 2)
+]
+
+# Farben für die drei Nullstellen (Rot, Grün, Blau)
+root_colors = [
+    (255, 0, 0),
+    (0, 255, 0),
+    (0, 0, 255)
+]
+
+img = Image.new('RGB', (width, height), (0, 0, 0))
+pixels = img.load()
+
+for py in range(height):
+    for px in range(width):
+        # Koordinaten umrechnen (von -2 bis 2)
+        zx = -2.0 + (px / width) * 4.0
+        zy = -2.0 + (py / height) * 4.0
+        z = complex(zx, zy)
+
+        found = False
+        for n in range(max_iter):
+            if abs(z) < 0.000001: break  # Vermeidung von Division durch Null
+
+            # Newton-Schritt für f(z) = z^3 - 1
+            # Formel: z = z - f(z) / f'(z)  =>  z = z - (z^3 - 1) / (3 * z^2)
+            z_next = z - (z ** 3 - 1) / (3 * z ** 2)
+
+            # Prüfen, ob wir nah genug an einer der Wurzeln sind
+            for i, root in enumerate(roots):
+                diff = z_next - root
+                if abs(diff) < tolerance:
+                    # Farbe basierend auf der Wurzel, Helligkeit basierend auf Iterationen
+                    brightness = int(255 * (1 - n / max_iter))
+                    r, g, b = root_colors[i]
+                    pixels[px, py] = (
+                        int(r * (brightness / 255)),
+                        int(g * (brightness / 255)),
+                        int(b * (brightness / 255))
+                    )
+                    found = True
+                    break
+            if found: break
+            z = z_next
+
+img.save("newton_fractal.png")
+img.show()
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diff --git a/newton_fractal.png b/newton_fractal.png
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