A sequence of determinants of points along a Hilbert curve

dethilbert.py

#!/usr/bin/python3

import matplotlib.pyplot as plt

# Code adapted from https://en.wikipedia.org/wiki/Hilbert_curve
def rot( n, x, y, rx, ry ):
    if ry == 0:
        if rx == 1:
            x = (n-1) - x
            y = (n-1) - y

        # Swap x and y
        return (y,x)
    else:
        return (x,y)

def d2xy( n, d ):
    t = d
    x = y = 0
    s = 1
    while s < n:
        rx = 1 & (t//2)
        ry = 1 & (t ^ rx)
        (x,y) = rot(s, x, y, rx, ry)
        x += s * rx
        y += s * ry
        s *= 2
        t //= 4
    return (x,y)


def det( v1, v2 ):
    (a,b) = v1
    (c,d) = v2
    return a*d - b*c

n = 32
d = 0
v1 = d2xy( n, 0 )
print( v1 )

points = []
labels = []
points.append( v1 )

for d in range( 1, n**2+1 ):
    v2 = d2xy( n, d )
    points.append( v2 )
    t = det( v1, v2 )
    labels.append( (v2, t) )
    print( v2, t )
    v1 = v2

if n <= 32:
    plt.plot( [x for (x,y) in points[:-1]], [y for (x,y) in points[:-1]] )
    for p, l in labels: 
        plt.annotate( str(l), xy=p, xytext=(1,1), textcoords="offset points" )
    plt.show()

plt.plot( [d for (p,d) in labels], "r." )
plt.show()