This is some Perl code to calculate various mathematical paths through a 2-D X,Y plane, sending an index N to coordinates X,Y, or from coordinates to index.

13 14 3 12 ... 15 4 1 2 11 28 16 5 6 7 8 9 10 27 17 18 19 20 21 22 23 24 25 26

Read more on the general operation in the
`online man page`

and see the
full list of online man pages.

`Math-PlanePath`

is
free software (free
as in freedom), published under the terms of the
GNU
General Public License (v3 or higher).

Download version 129 here, either just
the `.pm`

file, the full source here or
from CPAN, or a
Debian package here or from my repo.

`Math-PlanePath-129.tar.gz`

(1507k, and sig)

`libmath-planepath-perl_129-0.1_all.deb`

(1199k, and sig)

Separate Math-PlanePath-Toothpick has toothpick and some more cellular patterns. Download version 18,

`Math-PlanePath-Toothpick-18.tar.gz`

(168k, and sig)

`libmath-planepath-toothpick-perl_18-0.1_all.deb`

(120k, and sig)

The sig files are Gnu PG ascii armoured
signatures generated from my key. There's a
`SIGNATURE`

file inside the `.tar.gz`

for
`cpansign`

too. Older sources can be found
at backpan.

There's no drawing in Math-PlanePath, just coordinate calculations (see math-image for drawing), but here's some samples. Each image is a link to its section in the gallery (PNG images, about 338k total).

- Square numbering of Ulam's spiral
- Hexagonal spirals
- Pentagonal, heptagonal, anvil and octagram spirals
- Diamond spiral and rings
- Triangle spirals
- Diagonals, corners, and staircases
- Pyramid side and rows, M peaks
- Cellular automaton patterns
- Infinite knight's tour and Cretan labyrinth
- Greek Key motif
- Multi-arm spirals
- Peano, Hilbert, Z-order, Gray code
- Wunderlich serpentine and meander, Beta-Omega, AR2W2, Kochel curves
- Dekking and Cinco curves
- Imaginary base, cubic base, corner replicate, square replicate
- L tiling, digit groups
- Fibonacci word fractal
- Vogel's sunflower floret
- Sacks' quadratic spiral
- Spiral of Theodorus and Archimedean Chords
- Pixellated, filled, and circular rings
- Flowsnake and Gosper islands
- Quintet
- Koch curve and snowflakes
- Quadric curve and islands
- Sierpinski triangle and arrowhead
- Sierpinski curve and H-indexing
- Dragon paper-folding and alternate paper folding, and their midpoints
- Terdragon curve, rounded, midpoints, and alternate terdragon
- R5dragon curve and midpoints
- Lévy C Curve
- Complex i+/-r (including twindragon i-1), and revolving i+1
- Points by hypotenuse distance square or triangular
- Pythagorean triples tree
- Rationals diagonal, factors, GCD, Cfrac digits
- Rationals, fractions, and Chan trees
- Coprime and divisible columns
- Ulam-Warburton cellular
- Wythoff and power arrays

And in the Math-PlanePath-Toothpick distribution,

See `math-image`

to display
various values on these these paths.

This page Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021 Kevin Ryde, except for the GPLv3 logo which is Copyright Free Software Foundation and used here in accordance with its terms.

Imagine this page spiralling.

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