r"""
Hilbert's space-filling curve
===================================

Draws the first few Hilbert curves, each visiting every cell of a
finer grid. In the limit the curve passes through every point of the
square while keeping nearby points of the curve close in the plane.
"""

# %%
import matplotlib.pyplot as plt

from mathematicskit.fractals_chaos import hilbert_curve

# %%
# Orders 1 to 5
# -----------------------------------------------------

fig, axes = plt.subplots(1, 5, figsize=(14, 3))
for ax, order in zip(axes, range(1, 6)):
    pts = hilbert_curve(order)
    n = 2**order
    ax.plot((pts[:, 0] + 0.5) / n, (pts[:, 1] + 0.5) / n, lw=1.2 if order < 4 else 0.6)
    ax.set_aspect("equal")
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.set_title(f"order {order}: {len(pts)} cells")
    ax.axis("off")

# %%
# Locality: nearby indices map to nearby cells
# -----------------------------------------------------

pts = hilbert_curve(6)
jumps = abs(pts[1:] - pts[:-1]).sum(axis=1)
print(f"order 6: {len(pts)} cells, every step moves to a neighbouring cell: {bool((jumps == 1).all())}")