DOC: add a fractal example

examples/mandelbrot.py

@@ -0,0 +1,50 @@
+"""
+===================================
+(Infinitly) Zoomable Mandelbrot Set
+===================================
+
+
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from data_prototype.wrappers import ImageWrapper
+from data_prototype.containers import FuncContainer
+
+from matplotlib.colors import Normalize
+
+maxiter = 75
+
+
+def mandelbrot_set(X, Y, maxiter, *, horizon=3, power=2):
+    C = X + Y[:, None] * 1j
+    N = np.zeros_like(C, dtype=int)
+    Z = np.zeros_like(C)
+    for n in range(maxiter):
+        I = abs(Z) < horizon
+        N += I
+        Z[I] = Z[I] ** power + C[I]
+    N[N == maxiter] = -1
+    return Z, N
+
+
+fc = FuncContainer(
+    {},
+    xyfuncs={
+        "xextent": ((2,), lambda x, y: [x[0], x[-1]]),
+        "yextent": ((2,), lambda x, y: [y[0], y[-1]]),
+        "image": (("N", "M"), lambda x, y: mandelbrot_set(x, y, maxiter)[1]),
+    },
+)
+cmap = plt.get_cmap()
+cmap.set_under("w")
+im = ImageWrapper(fc, norm=Normalize(0, maxiter), cmap=cmap)
+
+fig, ax = plt.subplots()
+ax.add_artist(im)
+ax.set_xlim(-1, 1)
+ax.set_ylim(-1, 1)
+ax.set_aspect("equal")
+fig.colorbar(im)
+plt.show()