Create app.py

app.py

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+"""
+## Explanation
+
+The *Mandelbrot set* is a fascinating two-dimensional fractal that is defined by a simple mathematical formula but exhibits remarkable complexity, especially when magnified. It is widely known for its intricate patterns and aesthetic appeal.
+
+The set is defined on the complex plane as the set of complex numbers $$ c $$ for which the iterative function $$ f_c(z) = z^2 + c $$ does not diverge to infinity when starting at $$ z = 0 $$. In other words, the sequence $$ f_c(0) $$, $$ f_c(f_c(0)) $$, and so on, remains bounded in absolute value.
+
+In this implementation, the sequence is computed iteratively. The process stops if the magnitude of the number exceeds 4, indicating that it has diverged. The color in the resulting image reflects the number of iterations needed to determine if the point belongs to the Mandelbrot set.
+"""
+
+import colorcet as cc
+import holoviews as hv
+import numpy as np
+import panel as pn
+from holoviews.streams import RangeXY
+from numba import jit
+
+pn.extension("mathjax")
+
+DEFAULT_COLOR_MAP = [
+    "#0b2f4c",  # Deep blue
+    "#164e80",  # Medium blue
+    "#208ed6",  # Bright blue
+    "#30a0e0",  # Aqua blue
+    "#71c4f2",  # Light sky blue
+    "#b4e4fa",  # Pale blue
+    "#f5f1b8",  # Soft yellow
+    "#f0c366",  # Light orange
+    "#f28d35",  # Bright orange
+    "#e0471e",  # Fiery red
+    "#a83e1c",  # Deep red-brown
+    "#662b12",  # Dark brown
+    "#2d1107",  # Almost black
+    "black",  # Pure black
+]
+ACCENT = DEFAULT_COLOR_MAP[1]
+
+
+@jit
+def mandel(x, y, max_iters):
+    """
+    Given the real and imaginary parts of a complex number,
+    determine if it is a candidate for membership in the Mandelbrot
+    set given a fixed number of iterations.
+    """
+    i = 0
+    c = complex(x, y)
+    z = 0.0j
+    for i in range(max_iters):
+        z = z * z + c
+        if (z.real * z.real + z.imag * z.imag) >= 4:
+            return i
+
+    return 255
+
+
+@jit
+def create_fractal(min_x, max_x, min_y, max_y, image, iters):
+    height = image.shape[0]
+    width = image.shape[1]
+
+    pixel_size_x = (max_x - min_x) / width
+    pixel_size_y = (max_y - min_y) / height
+    for x in range(width):
+        real = min_x + x * pixel_size_x
+        for y in range(height):
+            imag = min_y + y * pixel_size_y
+            color = mandel(real, imag, iters)
+            image[y, x] = color
+
+    return image
+
+
+def get_fractal(x_range, y_range, iters=200, cmap="set1", width=1200, height=1200):
+    (x0, x1), (y0, y1) = x_range, y_range
+    image = np.zeros((width, height), dtype=np.uint8)
+    return hv.Image(
+        create_fractal(x0, x1, -y1, -y0, image, iters), bounds=(x0, y0, x1, y1), rtol=1e-9
+    ).opts(
+        colorbar=True,
+        cmap=cmap,
+        xlabel="Real",
+        ylabel="Imaginary",
+        title="Complex Plane",
+        clabel="Number of Iterations",
+        clim=(0, 255),
+        tools=["hover"],
+    )
+
+
+range_stream = RangeXY(x_range=(-1.0, 1.0), y_range=(-1.0, 1.0))
+
+max_iterations = pn.widgets.IntSlider(value=200, start=1, end=254, name="Max Iterations")
+
+height = pn.widgets.IntSlider(
+    value=800,
+    start=100,
+    end=2000,
+    name="Image height (pixels)",
+)
+width = pn.widgets.IntSlider(
+    value=1000,
+    start=100,
+    end=2000,
+    name="Image width (pixels)",
+)
+
+
+palette = {"default": DEFAULT_COLOR_MAP}
+palette.update(cc.palette)
+cmap = pn.widgets.ColorMap(
+    value=DEFAULT_COLOR_MAP,
+    options=palette,
+    ncols=3,
+    swatch_width=100,
+    sizing_mode="stretch_width",
+    name="Color Map",
+)
+dmap = hv.DynamicMap(
+    pn.bind(
+        get_fractal,
+        iters=max_iterations,
+        x_range=range_stream.param.x_range,
+        y_range=range_stream.param.y_range,
+        cmap=cmap,
+        height=height,
+        width=width,
+    )
+)
+dmap_panel = pn.panel(dmap, height=height, width=width)
+pn.template.FastListTemplate(
+    site="Awesome Panel",
+    site_url="./",
+    title="Mandelbrot",
+    sidebar=["## Settings", cmap, max_iterations, height, width, pn.pane.Markdown(__doc__)],
+    main=[dmap_panel],
+    accent=ACCENT,
+    main_layout=None,
+).servable()