General SG programs:

diffsg:	This is a function to calculate derivatives of the map f: R^m1 -> R^m2 defined by restricting an (m1)st level complex of delta circuits to an (m2)nd level one. We approximate derivatives with respect to perturbing each edge, and for each edge in the restriction, using difference quotients with a variety of sizes of perturbation
eip.m	Computes the energy inner product of two functions on SG
emeasure	Computes energy measure for a given harmonic function and cell
energy	Computes energy of a function
f0	A contractive similarity of the plane centered at 0 of dilation factor 1/2
fi	A contractive similarity of the plane centered at the point qi of dilation factor 1/2
findps	Returns relative coordinates to use when printing out a table of values at vertex points on SG
gaskplot	Plots a function defined on the level m vertices of SG, with edges connecting adjacent vertices
harm	Computes the harmonic extension from V_0 to V_1 of a harmonic function.
harmonic	Computes the harmonic extension (given boundary points) to a particular level
kusuoka:	Calculates the Kusuoka measure of a cell
plotemeasure	Plots the values of an energy measure
plotkusuoka	Plots the Kusuoka measure
radon	Calculates the Radon-Nikodym derivative of an energy measure with respect to the Kusuoka measure
qcontract	Applies the function fi to a column of coordinate pairs
SGdata	A reference file with some important matrices for SG
SGedges	Computes the coordinates of the midpoints of all level m edges of SG
sgyprint	Prints the values of a function on the vertices of SG
Wordm	Performs a sequence of contractions on a set of vectors (in a matrix) in $R^{2}$ given a word w
Wordv	Performs a sequence of contractions on a vector given a word w

Indexing:

wordmatrix	Gives a matrix of all words of length m consisting of 0,1,2
address	Returns a vector listing the address of a given index k in a level m SG-type ordering (TLR ordering)
alternateaddress	Finds the alternative address for a given point in an SG ordering
alternateindex	Finds the alternative index for a given point in TLR ordering on SG.
indexsg	Finds the index in TLR ordering corresponding to a given address
gneighbors	This function finds the addresses of those edges which are incident to a given vertex
mindices.m	A headache-saving formula for the jth group of 3^m consecutive indices
mixup	Accepts a vector $y$ of size 3^m1, for some m1, and a permutation $indices$ of size 3^m2, for m2 <= m1, and scrambles the 3^m2 subvectors of y (each of size 3^(m1-m2)) according to the permutation
permutecells	Composes a function f:SG->R with a permutation of the cells of SG
reorder	Just a simple function to reorder a vector from largest to smallest element
singleindices	Solves the problem of performing calculations such as computing the spectrum of the Laplacian on SG when our chosen data storage scheme is redundant
vneighbors	Finds the addresses of those edges which are incident to a given vertex

Graph restrictions and their relation to the Kusuoka measure:

dergraph	Plots derivatives of resistances of restriction of graph after perturbing an edge
derword	Computes derivative measures
doword	Computes measures on all cells of a level m graph
ds	Compute the derivatives of the resistances of the restricted graph with respect to perturbing each edge individually by a small t (see inside comments on how we use 3^m by 3 matrices in describing Y-networks
dy	Performs Delta-Y transformation on resistances of a Delta graph.
net	Produces coordinates of edges of Y-network of level m.
ninetothree	A level 1 Y-network of resistors to a single Y-circuit
omatrix	Gives a matrix with zeros everywhere except at one specified entry
plotder	Plots derivatives of resistances of Y graph after perturbing edges of an m-cell of the level m Y-network.
plotpert	Plots derivatives when only perturbing an edge.
radonder	Calculates radon-nikodym derivative of the derivative measures with respect to the Kusuoka measure.
rcol	Produces a concatenation of each step of the restriction of a system of resistors on SG (in Y-circuits)
restrict	This function computes the restriction of an (m1)st level network of resistors to an (m2)nd level such network, where a network at the mth level is the stacking of three (m-1)st level networks, and a 1st level network is a Y shaped network.
restrictall	Computes the restriction of a level m Y-network of resistors on SG to a single Y-circuit on the boundary points of SG.
restrictseq	Stores the intermediate computations involved in restricting a function between two levels of a Y-circuit. (Note: The point of this is that if you want to perform a restriction of a function that is perturbed on only one cell, you can save computation by simply executing this function ahead of time and, instead of doing redundant calculations, simply reading the restriction data for all cells not containing the perturbed cell since those remain unchanged).
smartrestrict	This is a computation-saving program for calculating restrictions of Y-networks of resistors. Performs the restriction of an m1-level SG-circuit to an m2-level circuit.
ydelta	Finds the delta-circuit of resistors on three vertices which is equivalent to an inputed y-circuit on the same three vertices with a central fourth vertex added.

Laplacians on the Sierpinski Gasket

claplacian	Calculates the Laplacian of 1 (the constant function).
defnstep:	Defines a step function on a level m graph approximation of SG.
deltarestrict	Restricts a Delta network of resistors
deltay	Computes a Y network equivalent to a (single) given Delta network of resistors.
diffquot	Computes a difference quotient approximation to a directional derivative of the map f: R^{m1} -> R^{m2} which takes a level m1 Delta network of resistors and restricts to a level m2 network.
diffquotSeq	This is a computation-saving version of diffquot.m (runs much faster for m1 >= 7 or so).
doetaplot	Makes a plot of the Weyl ratio for a computed spectrum, which is assumed to be stored as the variable “cspec”.
doplot	Once you have computed the spectrum of a conformal Laplacian, doplot allows you to create a plot of the Weyl file.
doSGweylratioplots	Script to print out pictures of several Weyl ratio plots.
dospectrum	Script to calculate the spectrum for the Dirichlet Laplacian, assuming a conformal factor g and level m are given.
dostepfunc	This is what I used to make conformal factors to put on SG. I tried to come up with some wavy sinusoidal thing that wouldn’t have any symmetry.
dsplaplacian	Returns the Dirichlet spectrum of the Laplacian for the conformal factor g using level m approximation.
edgefunc	Allows one to define an edge function on SG by inputting a function on R^2, and calculating the value of the function at the midpoint of each edge, where we use embedding of SG into R^2 such that the vertices form equilateral triangles.
edgeplot	Creates a graphic plot of a level m edge function on SG.
flaplacian	This function takes an inline function of the plane and computes its values at level m vertex points on a certain embedding of SG in the plane (as in an equilateral triangle with boundary points (0,0), (1/2,sqrt(3)/2),and (sqrt(3)/2,1/2)), then takes the level m laplacian of the resulting function and produces a plot of it.
formatcurrentSGweylratioplot	Labels the current Weyl ratio plot with ‘log(x)’ on the x-axis and ‘N(x)/x^\beta’ on the y-axis.
formattedratio	Changes a decimal number into a standard format to append to a file name.
funcdefn	This function allows the inputing of an R^2 function whose value to find on the junction points of a certain embedding of SG into the plane.
laplacian	This function accepts a function $u$ stored as a vector of length $3^(m+1)$ and a conformal factor $g$ of the same length, and computes the g-laplacian of u.
makeSGweylratioplot	Script to make a plot of the Weyl ratio for a conformal Laplacian once the spectrum has been computed
mlaplacian	Calculates the matrix corresponding to the Weyl ratio
nsplaplacian	This function computes the Neumann spectrum of the conformal laplacian with factor g size of g = 3^(m+1)
printcurrentSGweylratioplot	Script to print the current Weyl ratio plot under a coherent naming scheme
ptlaplacian	Calculates the laplacian of a function at a single point
spectralgaps	Calculates the gaps between subsequent eigenvalues of the Laplacian.

Miscellaneous:

clover	Plots Vicek graphs
log3	computes log base 3.
pdim	computes p dimension of an energy measure.
plot3c	does color point plot (Matlab only does color plot in the meshplot, as far as I know).
reorder	reorders a vector of values.
tenergy	computes energy of functions on the tetrahedral Sierpinski Gasket.
tetraSG	plots tetrahedral Sierpinski Gasket.
loopprint	allows printing of a table of values into an SG-type arrangement.
pdim	computes L_p dimensions.