## Simulations of Percolation on the Hexagonal Lattice

**Last modified**: May 23, 2008

Here is code to generate pictures of critical site percolation on the hexagonal lattice (i.e., each hexagon is coloured either red or white independently with probability 1/2).

This code was written by my colleague Edward Doolittle of the University of Regina.

It is written in Asymptote and can either be run directly with the Asymptote program or included in a LaTeX document.

### Instructions for running percolate1.asy directly

**Step 0:** Make sure that Asymptote is installed on your system. See the Asymptote website for more details.

**Step 1:** Run the command asy on the file percolate1.asy. The output is the file percolate1.eps in the same directory as where you ran asy.

> asy percolate1.asy

Read the percolationsample.ps or percolationsample.pdf file for a couple of tips on changing the percolate1.asy code to make different pictures.
**Step 2:** The .eps file can be included in your LaTeX document using \includegraphics{percolate1.eps} (or whatever other command you prefer to include .eps files). Or you can convert it to .pdf using epstopdf and \includegraphics the .pdf file.

### Instructions for including percolate1.asy in a LaTeX Document

**Step 0:** Make sure that Asymptote is installed on your system. See the Asymptote website for more details.

**Step 1:** Include the asymptote.sty package in your preamble.

**Step 2:** Use the asy environment and include the percolate1.asy code within the asy environment.

**Step 3:** Process your LaTeX file with three runs

> latex filename

> asy filename

> latex filename
or

> pdflatex filename

> asy filename

> pdflatex filename

Here is the sample LaTeX document percolationsample.tex illustrating the use of percolate1.asy.

percolationsample.tex

percolationsample.ps

percolationsample.pdf

### Several pictures for you to download

JPEG, 40 hexagons x 40 hexagons

JPEG, 40 hexagons x 40 hexagons

EPS, 20 hexagons x 30 hexagons

PDF, 20 hexagons x 30 hexagons

EPS, 17 hexagons x 12 hexagons

PDF, 17 hexagons x 12 hexagons

EPS, 17 hexagons x 12 hexagons (fixed boundaries)

PDF, 17 hexagons x 12 hexagons (fixed boundaries)

EPS, 37 hexagons x 30 hexagons

EPS, 47 hexagons x 37 hexagons

EPS, 37 hexagons x 30 hexagons (grid only)

EPS, 47 hexagons x 37 hexagons (grid only)

EPS, 30 hexagons x 30 hexagons

EPS, 50 hexagons x 50 hexagons (4 inch square)

EPS, 50 hexagons x 50 hexagons (6 inch square)

EPS, 100 hexagons x 100 hexagons (4 inch square)

EPS, 100 hexagons x 100 hexagons (6 inch square)

EPS, 100 hexagons x 100 hexagons (8 inch square)

*Michael's Home Page* * *U of R Math & Stats Department*

*May 23, 2008*