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Python, pasted on Oct 16: 
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import numpy as np
import matplotlib.pyplot as plt

points = np.array([
 [0.8660254037844384, -0.5000000000000004],
 [0.7577722283113836, -0.5000000000000004],
 [0.6495190528383288, -0.5000000000000003],
 [0.5412658773652739, -0.5000000000000003],
 [0.4330127018922191, -0.5000000000000002],
 [0.3247595264191642, -0.5000000000000002],
 [0.21650635094610943, -0.5000000000000002],
 [0.10825317547305463, -0.5000000000000001],
 [-2.220446049250313e-16, -0.5000000000000001],
 [-0.10825317547305507, -0.5],
 [-0.21650635094610993, -0.5],
 [-0.32475952641916467, -0.5],
 [-0.4330127018922195, -0.4999999999999999],
 [-0.5412658773652743, -0.4999999999999999],
 [-0.6495190528383291, -0.49999999999999983],
 [-0.7577722283113839, -0.4999999999999998],
 [-0.8660254037844388, -0.4999999999999997],
 [0.811898816047911, -0.40625000000000044],
 [0.7036456405748561, -0.4062500000000004],
 [0.5953924651018013, -0.40625000000000033],
 [0.48713928962874653, -0.4062500000000003],
 [0.3788861141556917, -0.4062500000000002],
 [0.2706329386826369, -0.4062500000000002],
 [0.16237976320958203, -0.4062500000000001],
 [0.05412658773652723, -0.4062500000000001],
 [-0.05412658773652762, -0.40625000000000006],
 [-0.16237976320958242, -0.40625],
 [-0.2706329386826372, -0.40625],
 [-0.37888611415569207, -0.40624999999999994],
 [-0.4871392896287469, -0.4062499999999999],
 [-0.5953924651018018, -0.40624999999999983],
 [-0.7036456405748566, -0.4062499999999998],
 [-0.8118988160479114, -0.4062499999999997],
 [0.7577722283113836, -0.3125000000000004],
 [0.6495190528383288, -0.31250000000000033],
 [0.541265877365274, -0.31250000000000033],
 [0.4330127018922191, -0.3125000000000002],
 [0.3247595264191643, -0.3125000000000002],
 [0.21650635094610948, -0.31250000000000017],
 [0.10825317547305463, -0.3125000000000001],
 [-1.6653345369377348e-16, -0.31250000000000006],
 [-0.10825317547305502, -0.3125],
 [-0.21650635094610982, -0.3125],
 [-0.3247595264191646, -0.31249999999999994],
 [-0.43301270189221946, -0.3124999999999999],
 [-0.5412658773652743, -0.31249999999999983],
 [-0.6495190528383292, -0.3124999999999998],
 [-0.7577722283113839, -0.3124999999999998],
 [0.7036456405748562, -0.21875000000000036],
 [0.5953924651018013, -0.2187500000000003],
 [0.48713928962874653, -0.21875000000000028],
 [0.37888611415569173, -0.21875000000000022],
 [0.2706329386826369, -0.21875000000000017],
 [0.16237976320958208, -0.21875000000000014],
 [0.05412658773652723, -0.21875000000000008],
 [-0.054126587736527565, -0.21875000000000006],
 [-0.16237976320958242, -0.21875],
 [-0.2706329386826372, -0.21874999999999994],
 [-0.378886114155692, -0.21874999999999992],
 [-0.48713928962874686, -0.21874999999999986],
 [-0.5953924651018017, -0.2187499999999998],
 [-0.7036456405748566, -0.21874999999999978],
 [0.6495190528383288, -0.12500000000000033],
 [0.541265877365274, -0.12500000000000028],
 [0.43301270189221913, -0.12500000000000025],
 [0.32475952641916433, -0.1250000000000002],
 [0.2165063509461095, -0.12500000000000017],
 [0.10825317547305469, -0.1250000000000001],
 [-1.6653345369377348e-16, -0.12500000000000006],
 [-0.10825317547305496, -0.125],
 [-0.21650635094610982, -0.12499999999999997],
 [-0.3247595264191646, -0.12499999999999993],
 [-0.4330127018922194, -0.12499999999999989],
 [-0.5412658773652743, -0.12499999999999983],
 [-0.6495190528383291, -0.12499999999999979],
 [0.5953924651018014, -0.031250000000000305],
 [0.4871392896287466, -0.03125000000000028],
 [0.37888611415569173, -0.031250000000000194],
 [0.27063293868263694, -0.03125000000000017],
 [0.1623797632095821, -0.03125000000000014],
 [0.05412658773652729, -0.03125000000000008],
 [-0.054126587736527565, -0.03125000000000003],
 [-0.16237976320958236, -0.031249999999999986],
 [-0.2706329386826372, -0.031249999999999944],
 [-0.378886114155692, -0.031249999999999903],
 [-0.4871392896287468, -0.031249999999999854],
 [-0.5953924651018017, -0.03124999999999981],
 [0.541265877365274, 0.06249999999999972],
 [0.4330127018922192, 0.06249999999999975],
 [0.3247595264191644, 0.06249999999999983],
 [0.21650635094610954, 0.06249999999999986],
 [0.10825317547305471, 0.06249999999999989],
 [-1.1102230246251565e-16, 0.062499999999999944],
 [-0.10825317547305496, 0.0625],
 [-0.21650635094610976, 0.06250000000000003],
 [-0.3247595264191646, 0.06250000000000008],
 [-0.4330127018922194, 0.06250000000000012],
 [-0.5412658773652742, 0.06250000000000017],
 [0.4871392896287466, 0.15624999999999975],
 [0.3788861141556918, 0.15624999999999978],
 [0.27063293868263694, 0.15624999999999986],
 [0.16237976320958214, 0.1562499999999999],
 [0.054126587736527315, 0.15624999999999992],
 [-0.05412658773652751, 0.15625],
 [-0.16237976320958236, 0.15625000000000003],
 [-0.27063293868263716, 0.15625000000000006],
 [-0.378886114155692, 0.1562500000000001],
 [-0.4871392896287468, 0.15625000000000017],
 [0.43301270189221924, 0.24999999999999978],
 [0.3247595264191644, 0.2499999999999998],
 [0.21650635094610957, 0.2499999999999999],
 [0.10825317547305474, 0.24999999999999992],
 [-8.326672684688674e-17, 0.24999999999999994],
 [-0.10825317547305491, 0.25],
 [-0.2165063509461097, 0.25000000000000006],
 [-0.32475952641916456, 0.2500000000000001],
 [-0.43301270189221935, 0.2500000000000001],
 [0.37888611415569184, 0.3437499999999998],
 [0.270632938682637, 0.34374999999999983],
 [0.16237976320958217, 0.3437499999999999],
 [0.05412658773652734, 0.34374999999999994],
 [-0.05412658773652748, 0.34375],
 [-0.1623797632095823, 0.34375000000000006],
 [-0.2706329386826371, 0.3437500000000001],
 [-0.37888611415569196, 0.3437500000000001],
 [0.32475952641916445, 0.43749999999999983],
 [0.2165063509461096, 0.4374999999999999],
 [0.10825317547305478, 0.4374999999999999],
 [-5.551115123125783e-17, 0.4374999999999999],
 [-0.10825317547305488, 0.43750000000000006],
 [-0.2165063509461097, 0.4375000000000001],
 [-0.3247595264191645, 0.4375000000000001],
 [0.27063293868263705, 0.5312499999999999],
 [0.1623797632095822, 0.5312499999999999],
 [0.054126587736527385, 0.5312499999999999],
 [-0.054126587736527426, 0.53125],
 [-0.16237976320958225, 0.5312500000000001],
 [-0.2706329386826371, 0.5312500000000001],
 [0.21650635094610965, 0.6249999999999999],
 [0.10825317547305482, 0.6249999999999999],
 [-1.3877787807814457e-17, 0.625],
 [-0.10825317547305482, 0.625],
 [-0.21650635094610965, 0.6250000000000001],
 [0.16237976320958225, 0.7187499999999999],
 [0.05412658773652742, 0.71875],
 [-0.0541265877365274, 0.71875],
 [-0.16237976320958222, 0.71875],
 [0.10825317547305485, 0.8125],
 [2.7755575615628914e-17, 0.8125],
 [-0.1082531754730548, 0.8125],
 [0.054126587736527454, 0.90625],
 [-0.05412658773652737, 0.90625],
 [6.123233995736766e-17, 1.0]])

def test1(x=None):
    # Failure for x > 23
    slc = slice(None,x,None)
    plt.scatter(points[slc,0], points[slc,1])
    matplotlib.delaunay.Triangulation(points[slc,0], points[slc,1])
    
def test2(x=None):
    # Randomizing the rows seems to have no effect
    # Failure for x > 23
    slc = slice(None,x,None)    
    idx = np.arange(points.shape[0])
    np.random.shuffle(idx)
    points2 = np.array([points[i] for i in idx])
    plt.scatter(points2[slc,0], points2[slc,1])
    matplotlib.delaunay.Triangulation(points[slc,0], points[slc,1])    

if __name__ == '__main__':
    test2()


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