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Archives

This page contains links to various scripts and databases used to investigate tilings on surfaces. The archives are organized by the background notes and the various project areas as in the jump table below. In a project area the files are organized into data folders, script folders (including function libraries, intermediate output files and log files) or image folders. The more important files will have direct links, other links will simply take you to the appropriate folder. In the jump table the interpretation of various extensions is explained; only .mws, .m  and .mat are standard. All files except Matlab data files, are simple text files. A library script or function library file is a package of related functions readable by the appropriate application, say Maple or Magma.
Jump and Information Table
Background Notes Research Project Areas File Extension Interpretation
image scripts
various constructions

low genus classification
- triangles
- quadrilaterals
divisible tilings
geodesics, length spectrum and billiards
moduli
ovals
separability of symmetries
separability of symmetries - graphs
tiler (create tilings with Matlab)

.mws Maple worksheet,
.mpl Maple scripts and Maple library scripts
.m     Matlab script
.mat Matlab data file
.mgm Magma scripts and library scripts
.act .bdat .dat .rez various data files (text)
.log transcript file
.eps encapsulated post script

Background Notes - Scripts

Producing Images

Image drawing scripts - folder
icos.mws icosahedral tiling of the sphere
torus244.mws (2,4,4) tiling on the torus
torus333.mws (3,3,3) tiling on the torus
genus2.mws surface of genus two
triang4.mws master tile (needs gtools.mpl)

Various Constructions and Derivations

Other scripts for notes - folder
Hgeom.mws Geometric constructions
DHgeom.mws Invariance and distance calculations for the disc
UHgeom.mws Invariance and distance calculations for the upper half plane
NSchwartz.mws Numerical calculations for Schwartz triangles
schwartz.mws Symbolic Calculations for Schwartz triangles

Project Scripts and Data

Low genus classification of tilings and branching data for tilings

Triangle tilings
Data Folder (also contains some branching data files)
abelian2.act
cyclic.act
perm.act
pgroupNA.act
solvableNANP.act
two generator abelian rotation group actions
cyclic group rotation group actions
non-solvable rotation group actions
non-abelian p-group rotation group actions
non-abelian non-p-group solvable rotation group actions

Scripts Folder (also contains some branching data input files)
A5.mgm sample script to find (2,3,5) - tilings of the sphere with G = Alt(5),
tileclass.mgm function library for computing tilings and calculating "theta"
tilerun.mgm
abelian2.mgm
cyclic.mgm
perm.mgm
pgroupNA.mgm
solvableNANP.mgm
master driver for tiling classification program
find two generator abelian rotation groups
find cyclic groups rotation groups
find non-solvable rotation groups (permutation group format)
find non-abelian p-group rotation groups (PC format)
find non-abelian non-p-group solvable rotation groups (PC format)
Quadrilaterals Tilings
Data Folder
Files are the form quads.vectors where s is the genus. Each entry contains branching data, group presentation, generating vectors and tiling status of the (k,l,m,n), ( k,m,l,n), and (k,l,n,m) twist of a generating vector .
Scripts Folder (also contains some branching data input files)
quadclass.mgm function library for computing tilings and calculating "theta"
quadrun.mgm master driver for tiling classification program
Branching data
Data and Script Folder
bradatpoly.mws
branching data for small polygons and low genus

Divisible Tilings

The final images for the divisible tilings were constructed from the intermediate result files listed here and the Matlab tiling scripts, also listed here.
Data and Images Folders
Boundary Construction .rez and .log files containing information on all divisible
quadrilaterals constructible by boundary construction method
Direct Construction .mpl files containing information on all divisible quadrilaterals
constructible by direct construction method
Images folder containing divisible quadrilaterals constructible by direct
construction methods as .mpl files

Scripts Folder
tiling m-file folder folder of Matlab scripts to that draw tilings by triangles
Boundary Construction folder of Maple scripts to determine divisible quadrilaterals
by boundary construction method (also contains log and rez files)
Direct Construction folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as .mpl files)

Geodesics, Length Spectrum of a Surface and Billiards

Scripts Folder
Data Folder (reduced words for translations and glides)
Images Folder (billiards, .eps files)
NSchwartz.mws numerical calculations for Schwartz triangles
billiardpics.mws billiard drawing program for figures
billiardtest.mws billiard drawing program with various tests
billiardsearch.mgm Magma program to find gernating words for billiards

Moduli

Scripts Folder
permtoLFT.mws permutation action on the quotient spaces

Ovals and Oval Intersections

Scripts Folder
ovalfunc.mgm oval intersection functions
ovalint.mgm sample oval intersection calculations

Separability of Symmetries

Scripts Folder
IsSplit.mgm determines whether a tiling is split
IsSplitS.mgm a tweaked version of IsSplit.mgm

Separability of Symmetries - uing graphs


Scripts Folder, Data folder, Genus Data Folder
Group.mgm Compute separability for all reflections for a given group, using Reflective Walk Algorithm
GroupS.mgm Compute separability for all reflections for a given group, using modified Reflective Walk Algorithm
Graph.mgm Compute separability for all reflections for a given group, using Cayley Line Graph

Tilings with Matlab

The scripts in this folder allow one to create and draw triangular tilings, according to a tiling word. The main scripts are mtess.m for creating tiling words and ttess.m for drawing tilings according to a word.
Scripts Folder
mtess.m oval intersection functions
ttess.m sample oval intersection calculations

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Send questions and comments to: allen.broughton@rose-hulman.edu
Last modified December 28, 2000