(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 136507, 3568] NotebookOptionsPosition[ 135162, 3516] NotebookOutlinePosition[ 135505, 3531] CellTagsIndexPosition[ 135462, 3528] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Pascal\[CloseCurlyQuote]s Triangle Fractals", "Title", CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { 3.7766384838213315`*^9, 3.776638488819731*^9}}], Cell["Adam Rumpf, 6/28/2015", "Text", CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { 3.7766384931880608`*^9, 3.7766384964870157`*^9}}], Cell[CellGroupData[{ Cell["Introduction", "Section", CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], Cell[TextData[{ "This Notebook contains a variety of functions for generating graphics of \ Pascal\[CloseCurlyQuote]s triangle. The ", StyleBox["pascal[]", "Code"], " function simply displays Pascal\[CloseCurlyQuote]s triangle with a \ specified number of rows and with the numbers filled in. The ", StyleBox["parity[]", "Code"], " function accepts arguments for a number of rows and a base, and displays \ Pascal\[CloseCurlyQuote]s triangle colored so that the entries divisible by \ the chosen base are blank while the rest are black." }], "Text", CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { 3.7766397314080024`*^9, 3.7766399513305798`*^9}}], Cell[TextData[{ "The main motivation for these functions is to see the fractal structures \ present in Pascal\[CloseCurlyQuote]s triangle. Speficically, highlighting \ only the odd entries creates a Sierpi\:0144ski triangle. This corresponds to \ using the above ", StyleBox["parity[]", "Code"], " function with a base of ", Cell[BoxData[ FormBox["2", TraditionalForm]], FormatType->"TraditionalForm"], ". 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