Create a new workbook

Make sure that zeros are displayed as whitespace:

- \File\Options

- Select 'Advanced' on left sidebar

- ( Look for 'Display options for this worksheet: Sheet1' )

- When found deselect 'Show a zero in cells that have a zero value'

Set the column-width to the first 130 rows or so to about 3.0

Now apply some values to the following four cells.

A1: p ( any prime ), use a small prime, for example 3.

C3: 1

A4: =A3+1 ( not necessary, but shows interesting properties )

In C4 we implement the Pascal recurrence modulo a prime

C4: =MOD(C3+B3;*A*1) ( replace * with dollar sign conflict with MathJax )

Now you have to do some copying and pasting:

- you have to copy this cell at least 128 cells to the right

- copy the contents of row 4 at least 127 times

If you have done this correct you will see patterns like this:

Mod 2, zoom 30% |

Mod 3, zoom 30% |

Mod 7, zoom 30% |

It should be possible to control graphics at the pixel level with Mathematica, I might give it a try.

It was OU course M381 ( which I am on at the moment ) that gave me the idea to look at the Pascal triangle modulo a prime because one of the topics in M381 is the Fibonacci series modulo a prime. The Pascal Triangle and the Fibonacci series are definitely among my favourite mathematical objects. If I had to choose I would say the PT of course, because the Fibonacci series is neatly contained within it. What is not? One might ask.

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