Matlab Programs
The Matlab functions are used to graph the functions on the Sierpinski Gasket, the edge plots, and the zero plots. The recurrence relation and dynamics plots were all done in Mathematica.
Main OP Functions
Start with SGplotsOverview.m as a tutorial for using the Matlab plotting functions.
| Program | Description |
|---|---|
| edgeplots | Makes the plots of the OP restricted to the edges |
| edgezeros4 | Finds the zeros on the bottom edge of OP |
| edgezerosplots | Plots the results of edgezeros4.m |
| getOmegas3 | Reads values of the Antisymmetric (normalized) OP |
| getOmegas5 | Reads values of the Symmetric (normalized) OP |
| getorder | Helper function for readPolys.m to reorder function value points from polydata_20.txt |
| monomialplots | Graphs the monomials |
| onbplots | Graphs the completely orthonormal polynomials |
| orthoplotspk | Graphs the Antisymmetric OP |
| orthoplotssk | Graphs the Symmetric OP |
| readPolys | Reads in the values of the monomials. |
| SGcontour | plots a countour plot of the function u |
| SGcontourplots | Uses SGcontour.m to make the zero plots for the Antisymmetric and Symmetric OP |
| SGedge13 | Finds the indices of the side edge in SG. |
| SGedge23 | Finds the indices of the bottom edge in SG. |
| SGorthoPolyEdge13phik | Finds the values of the Fully Orthonormal Polynomials along the side edge. |
| SGorthoPolyEdge13pk | Finds the values of the Antisymmetric OP along the side edge. |
| SGorthoPolyEdge23phik | Finds the values of the Fully Orthonormal Polynomials along the bottom edge. |
| SGorthoPolyEdge23pk | Finds the values of the Antisymmetric OP along the bottom edge. |
| SGorthoPolyEdge23sk | Finds the values of the Symmetric OP along the bottom edge. |
| SGorthoPolyspk | Calculates the values of the Antisymmetric (normalized) OP |
| SGorthoPolyssk | Calculates the values of the Symmetric (normalized) OP |
| SGplotsOverview | Overview of all plotting functions and how to use them. |
| SGrotate1 | Rotates the indices of SG once CCW. |
| SGrotate2 | Rotates the indices of SG twice CCW (or once CW). |
| zeroflag | Helper function for SGcontour.m, used to determine a potential zero in the contour plot based on surrounding neighbors' values |
Graphing SG functions
Most of theses are borrowed from: Conformal Energies, Conformal Laplacian, and Energy Measures on the Sierpinski Gasket.
| Program | Description |
|---|---|
| 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. |
| fi | A contractive similarity of the plane centered at the point qi of dilation factor 1/2 |
| gaskplot | Plots a function defined on the level m vertices of SG, with edges connecting adjacent vertices |
| gneighbors | This function finds the addresses of those edges which are incident to a given vertex |
| indexsg | Finds the index in TLR ordering corresponding to a given address |
| junctionindex | Finds index in higher level of address in TLR |
| log3 | computes log base 3. |
| qcontract | Applies the function fi to a column of coordinate pairs. |
| SG | Helper function for gaskplot. |