Merge pull request #221 from realpython/mandelbrot

Mandelbrot

Author: gahjelle

mandelbrot-set-python/01_scatter_plot.py

@@ -0,0 +1,33 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+np.warnings.filterwarnings("ignore")
+
+
+def complex_matrix(xmin, xmax, ymin, ymax, pixel_density):
+    re = np.linspace(xmin, xmax, int((xmax - xmin) * pixel_density))
+    im = np.linspace(ymin, ymax, int((ymax - ymin) * pixel_density))
+    return re[np.newaxis, :] + im[:, np.newaxis] * 1j
+
+
+def is_stable(c, num_iterations):
+    z = 0
+    for _ in range(num_iterations):
+        z = z ** 2 + c
+    return abs(z) <= 2
+
+
+def get_members(c, num_iterations):
+    mask = is_stable(c, num_iterations)
+    return c[mask]
+
+
+if __name__ == "__main__":
+    c = complex_matrix(-2, 0.5, -1.5, 1.5, pixel_density=21)
+    members = get_members(c, num_iterations=20)
+
+    plt.scatter(members.real, members.imag, color="black", marker=",", s=1)
+    plt.gca().set_aspect("equal")
+    plt.axis("off")
+    plt.tight_layout()
+    plt.show()

mandelbrot-set-python/02_bw_plot.py

@@ -0,0 +1,32 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+np.warnings.filterwarnings("ignore")
+
+
+def complex_matrix(xmin, xmax, ymin, ymax, pixel_density):
+    re = np.linspace(xmin, xmax, int((xmax - xmin) * pixel_density))
+    im = np.linspace(ymin, ymax, int((ymax - ymin) * pixel_density))
+    return re[np.newaxis, :] + im[:, np.newaxis] * 1j
+
+
+def is_stable(c, num_iterations):
+    z = 0
+    for _ in range(num_iterations):
+        z = z ** 2 + c
+    return abs(z) <= 2
+
+
+def get_members(c, num_iterations):
+    mask = is_stable(c, num_iterations)
+    return c[mask]
+
+
+if __name__ == "__main__":
+    c = complex_matrix(-2, 0.5, -1.5, 1.5, pixel_density=512)
+
+    plt.imshow(is_stable(c, num_iterations=20), cmap="binary")
+    plt.gca().set_aspect("equal")
+    plt.axis("off")
+    plt.tight_layout()
+    plt.show()

mandelbrot-set-python/03_bw.py

@@ -0,0 +1,19 @@
+from PIL import Image
+
+from mandelbrot_01 import MandelbrotSet
+
+if __name__ == "__main__":
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20)
+
+    width, height = 512, 512
+    scale = 0.0075
+    BLACK_AND_WHITE = "1"
+
+    image = Image.new(mode=BLACK_AND_WHITE, size=(width, height))
+    for y in range(height):
+        for x in range(width):
+            c = scale * complex(x - width / 2, height / 2 - y)
+            image.putpixel((x, y), c not in mandelbrot_set)
+
+    image.show()

mandelbrot-set-python/04_grayscale.py

@@ -0,0 +1,20 @@
+from PIL import Image
+
+from mandelbrot_02 import MandelbrotSet
+
+if __name__ == "__main__":
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20)
+
+    width, height = 512, 512
+    scale = 0.0075
+    GRAYSCALE = "L"
+
+    image = Image.new(mode=GRAYSCALE, size=(width, height))
+    for y in range(height):
+        for x in range(width):
+            c = scale * complex(x - width / 2, height / 2 - y)
+            instability = 1 - mandelbrot_set.stability(c)
+            image.putpixel((x, y), int(instability * 255))
+
+    image.show()

mandelbrot-set-python/05_grayscale_smooth.py

@@ -0,0 +1,22 @@
+from PIL import Image
+
+from mandelbrot_03 import MandelbrotSet
+
+if __name__ == "__main__":
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20, escape_radius=1000)
+
+    width, height = 512, 512
+    scale = 0.0075
+    GRAYSCALE = "L"
+
+    image = Image.new(mode=GRAYSCALE, size=(width, height))
+    for y in range(height):
+        for x in range(width):
+            re = scale * (x - width / 2)
+            im = scale * (height / 2 - y)
+            c = complex(re, im)
+            instability = 1 - mandelbrot_set.stability(c, smooth=True)
+            image.putpixel((x, y), int(instability * 255))
+
+    image.show()

mandelbrot-set-python/06_viewport_pixel.py

@@ -0,0 +1,19 @@
+from PIL import Image
+from PIL import ImageEnhance
+
+from mandelbrot_03 import MandelbrotSet
+from viewport import Viewport
+
+if __name__ == "__main__":
+    print("This might take a while...")
+
+    mandelbrot_set = MandelbrotSet(max_iterations=256, escape_radius=1000)
+
+    image = Image.new(mode="L", size=(512, 512))
+    for pixel in Viewport(image, center=-0.7435 + 0.1314j, width=0.002):
+        c = complex(pixel)
+        instability = 1 - mandelbrot_set.stability(c, smooth=True)
+        pixel.color = int(instability * 255)
+
+    enhancer = ImageEnhance.Brightness(image)
+    enhancer.enhance(1.25).show()

mandelbrot-set-python/07_color_palette_matplotlib.py

@@ -0,0 +1,31 @@
+import matplotlib.cm
+from PIL import Image
+
+from mandelbrot_03 import MandelbrotSet
+from viewport import Viewport
+
+
+def paint(mandelbrot_set, viewport, palette, smooth):
+    for pixel in viewport:
+        stability = mandelbrot_set.stability(complex(pixel), smooth)
+        index = int(min(stability * len(palette), len(palette) - 1))
+        pixel.color = palette[index % len(palette)]
+
+
+def denormalize(palette):
+    return [
+        tuple(int(channel * 255) for channel in color) for color in palette
+    ]
+
+
+if __name__ == "__main__":
+    print("This might take a while...")
+
+    colormap = matplotlib.cm.get_cmap("twilight").colors
+    palette = denormalize(colormap)
+
+    mandelbrot_set = MandelbrotSet(max_iterations=512, escape_radius=1000)
+    image = Image.new(mode="RGB", size=(512, 512))
+    viewport = Viewport(image, center=-0.7435 + 0.1314j, width=0.002)
+    paint(mandelbrot_set, viewport, palette, smooth=True)
+    image.show()

mandelbrot-set-python/08_color_palette_custom.py

@@ -0,0 +1,32 @@
+from PIL import Image
+
+from mandelbrot_03 import MandelbrotSet
+from viewport import Viewport
+
+
+def paint(mandelbrot_set, viewport, palette, smooth):
+    for pixel in viewport:
+        stability = mandelbrot_set.stability(complex(pixel), smooth)
+        index = int(min(stability * len(palette), len(palette) - 1))
+        pixel.color = palette[index % len(palette)]
+
+
+def denormalize(palette):
+    return [
+        tuple(int(channel * 255) for channel in color) for color in palette
+    ]
+
+
+if __name__ == "__main__":
+    print("This might take a while...")
+
+    exterior = [(1, 1, 1)] * 50
+    interior = [(1, 1, 1)] * 5
+    gray_area = [(1 - i / 44,) * 3 for i in range(45)]
+    palette = denormalize(exterior + gray_area + interior)
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20, escape_radius=1000)
+    image = Image.new(mode="RGB", size=(512, 512))
+    viewport = Viewport(image, center=-0.75, width=3.5)
+    paint(mandelbrot_set, viewport, palette, smooth=True)
+    image.show()

mandelbrot-set-python/09_color_gradient.py

@@ -0,0 +1,50 @@
+import numpy as np
+from PIL import Image
+from scipy.interpolate import interp1d
+
+from mandelbrot_03 import MandelbrotSet
+from viewport import Viewport
+
+
+def paint(mandelbrot_set, viewport, palette, smooth):
+    for pixel in viewport:
+        stability = mandelbrot_set.stability(complex(pixel), smooth)
+        index = int(min(stability * len(palette), len(palette) - 1))
+        pixel.color = palette[index % len(palette)]
+
+
+def denormalize(palette):
+    return [
+        tuple(int(channel * 255) for channel in color) for color in palette
+    ]
+
+
+def make_gradient(colors, interpolation="linear"):
+    X = [i / (len(colors) - 1) for i in range(len(colors))]
+    Y = [[color[i] for color in colors] for i in range(3)]
+    channels = [interp1d(X, y, kind=interpolation) for y in Y]
+    return lambda x: [np.clip(channel(x), 0, 1) for channel in channels]
+
+
+if __name__ == "__main__":
+    print("This might take a while...")
+
+    black = (0, 0, 0)
+    blue = (0, 0, 1)
+    maroon = (0.5, 0, 0)
+    navy = (0, 0, 0.5)
+    red = (1, 0, 0)
+
+    colors = [black, navy, blue, maroon, red, black]
+    gradient = make_gradient(colors, interpolation="cubic")
+
+    num_colors = 256
+    palette = denormalize(
+        [gradient(i / num_colors) for i in range(num_colors)]
+    )
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20, escape_radius=1000)
+    image = Image.new(mode="RGB", size=(512, 512))
+    viewport = Viewport(image, center=-0.75, width=3.5)
+    paint(mandelbrot_set, viewport, palette, smooth=True)
+    image.show()

mandelbrot-set-python/10_color_hsb.py

@@ -0,0 +1,33 @@
+from PIL import Image
+from PIL.ImageColor import getrgb
+
+from mandelbrot_03 import MandelbrotSet
+from viewport import Viewport
+
+
+def hsb(hue_degrees: int, saturation: float, brightness: float):
+    return getrgb(
+        f"hsv({hue_degrees % 360},"
+        f"{saturation * 100}%,"
+        f"{brightness * 100}%)"
+    )
+
+
+if __name__ == "__main__":
+    print("This might take a while...")
+
+    mandelbrot_set = MandelbrotSet(max_iterations=20, escape_radius=1000)
+    image = Image.new(mode="RGB", size=(512, 512))
+    for pixel in Viewport(image, center=-0.75, width=3.5):
+        stability = mandelbrot_set.stability(complex(pixel), smooth=True)
+        pixel.color = (
+            (0, 0, 0)
+            if stability == 1
+            else hsb(
+                hue_degrees=int(stability * 360),
+                saturation=stability,
+                brightness=1,
+            )
+        )
+
+    image.show()