Curve catalog

Each drawing is the actual order-3 path (64 cells). The circle marks entry and the square exit. The caption gives the curve index, label, family and distinct kernel indices. Select a curve using its index, label or paper symbol.

The construction chapter explains how to read the families: proper curves use Hilbert kernels, improper curves use Liu4 kernels with reversal, and inhomogeneous curves mix kernel types within an assembly.

0: Hilbert, order 3
0: Hilbertproper; kernels 0
1: Moore, order 3
1: Mooreproper; kernels 0
2: Liu1, order 3
2: Liu1proper; kernels 0
3: Liu2, order 3
3: Liu2proper; kernels 0
4: Liu3, order 3
4: Liu3proper; kernels 0
5: Liu4, order 3
5: Liu4proper; kernels 0
6: Improper1, order 3
6: Improper1improper; kernels 5
7: Improper2, order 3
7: Improper2improper; kernels 5
8: Improper3, order 3
8: Improper3improper; kernels 5
9: Improper4, order 3
9: Improper4improper; kernels 5
10: Improper5, order 3
10: Improper5improper; kernels 5
11: Improper6, order 3
11: Improper6improper; kernels 5
12: Liu2+Liu4 #1, order 3
12: Liu2+Liu4 #1inhomogeneous; kernels 3, 5
13: Liu2+Liu4 #2, order 3
13: Liu2+Liu4 #2inhomogeneous; kernels 3, 5
14: Liu2+Liu4 #3, order 3
14: Liu2+Liu4 #3inhomogeneous; kernels 3, 5
15: Liu2+Liu4 #4, order 3
15: Liu2+Liu4 #4inhomogeneous; kernels 3, 5
16: Liu2+Liu4 #5, order 3
16: Liu2+Liu4 #5inhomogeneous; kernels 3, 5
17: Liu2+Liu4 #6, order 3
17: Liu2+Liu4 #6inhomogeneous; kernels 3, 5
18: Hilbert+Liu3 #1, order 3
18: Hilbert+Liu3 #1inhomogeneous; kernels 0, 4
19: Hilbert+Liu3 #2, order 3
19: Hilbert+Liu3 #2inhomogeneous; kernels 0, 4
20: Hilbert+Liu3 #3, order 3
20: Hilbert+Liu3 #3inhomogeneous; kernels 0, 4
21: Hilbert+Liu3 #4, order 3
21: Hilbert+Liu3 #4inhomogeneous; kernels 0, 4
22: Hilbert+Liu3 #5, order 3
22: Hilbert+Liu3 #5inhomogeneous; kernels 0, 4
23: Hilbert+Liu3 #6, order 3
23: Hilbert+Liu3 #6inhomogeneous; kernels 0, 4
24: Hilbert+Liu3 #7, order 3
24: Hilbert+Liu3 #7inhomogeneous; kernels 0, 4
25: Hilbert+Liu3 #8, order 3
25: Hilbert+Liu3 #8inhomogeneous; kernels 0, 4
26: Hilbert+Liu3 #9, order 3
26: Hilbert+Liu3 #9inhomogeneous; kernels 0, 4
27: Hilbert+Liu3 #10, order 3
27: Hilbert+Liu3 #10inhomogeneous; kernels 0, 4
28: Hilbert+Liu3 #11, order 3
28: Hilbert+Liu3 #11inhomogeneous; kernels 0, 4
29: Hilbert+Liu3 #12, order 3
29: Hilbert+Liu3 #12inhomogeneous; kernels 0, 4
30: Hilbert+Liu3 #13, order 3
30: Hilbert+Liu3 #13inhomogeneous; kernels 0, 4
31: Hilbert+Liu3 #14, order 3
31: Hilbert+Liu3 #14inhomogeneous; kernels 0, 4
32: Moore+Liu4 #1, order 3
32: Moore+Liu4 #1inhomogeneous; kernels 1, 5
33: Moore+Liu4 #2, order 3
33: Moore+Liu4 #2inhomogeneous; kernels 1, 5
34: Moore+Liu4 #3, order 3
34: Moore+Liu4 #3inhomogeneous; kernels 1, 5
35: Moore+Liu4 #4, order 3
35: Moore+Liu4 #4inhomogeneous; kernels 1, 5
36: Moore+Liu4 #5, order 3
36: Moore+Liu4 #5inhomogeneous; kernels 1, 5
37: Moore+Liu4 #6, order 3
37: Moore+Liu4 #6inhomogeneous; kernels 1, 5
38: Moore+Liu2+Liu4 #1, order 3
38: Moore+Liu2+Liu4 #1inhomogeneous; kernels 1, 3, 5
39: Moore+Liu2+Liu4 #2, order 3
39: Moore+Liu2+Liu4 #2inhomogeneous; kernels 1, 3, 5

Use a selection

import hilbertplot as hp

info = hp.curves.info(12)
assert info["kernels"] == [3, 5]
fig = hp.plot_curve(12, order=3, color="steelblue")
fig = hp.gallery([0, 1, 6, 12], order=3, color="steelblue")

proper(), improper(), homogeneous(), inhomogeneous(), closed() and generalizing() return lists of metadata dictionaries that can be passed directly to gallery(). by_kernels(3, 5) selects exactly that kernel set. The full metadata fields are documented under catalog queries.