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  Scripts
Producing Images
Various Constructions and Derivations
Project Scripts and Data
Low genus classification of tilings and branching
data for tilings
Triangle tilings
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 nonsolvable rotation groups (permutation group format)
find nonabelian pgroup rotation groups (PC format)
find nonabelian nonpgroup 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 . 

quadclass.mgm 
function library for computing tilings and calculating
"theta" 
quadrun.mgm

master driver for tiling classification
program


Branching data
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 mfile 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
Moduli
Ovals and Oval Intersections
Separability of Symmetries
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.
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Send questions and comments to: allen.broughton@rosehulman.edu
Last modified December 28, 2000
