Here's a trick where you can appreciate the beauty of patterns in numbers.
Open a new worksheet in Excel.
On 'Sheet1', type "Mod:" into A1, and "2" into B1. On 'Sheet2', type the number "1" into A1. Copy the "1" down to about A999, so that you end up with a column full of 999 "1"s. (Don't go all the way down to the bottom, because you will run into memory problems later.)
Then on just the first row, copy the "1"s all the way across to column IV. Now you should have "1"s across the top, and "1"s going down the left side.
Now, the fun begins. In B2, type in the formula: =MOD(B1+A2,Sheet1!$B$1), and copy this formula into all cells in the rectangle B2:IV999. In case you're interested, you've just created a Pascal's Right Triangle using modular addition.
Highlight all columns (by clicking on the upper right-hand corner). Up in the column names, double click along one of the borders to resize all the columns. If you do it correctly, each cell should now be almost square.
Now, here's the dramatic part. Highlight the whole rectangle A1:IV999. In the menu, choose Format -> Conditional formatting. This will bring up a pop-up window.
Under Condition 1, the first selection menu should read "Cell Value Is." In the second selection menu, choose "equal to". In the third selection menu, type in the number "0".
Then click on Format. Another pop-up window will come up. At the top of this window, choose the Patterns tab. Then click on the color Black. Then OK.
This brings you back to the condition window. Click on Add, which will bring up Condition 2. Repeat the above steps to create the condition "Cell Value Is equal to 2", and choose your favorite color other than black or white.
Finally, click on Add again for Condition 3, and create the condition "Cell Value Is equal to <favorite number between 3 and 10>", and choose your second favorite color.
Hit OK to get out of the Conditional Formatting window, and see what the Formatting does. To fully appreciate the mathematical beauty, resize the whole Sheet2 to 50% or even 25%. Isn't that a great pattern?
Finally, on Sheet1, try different numbers in cell B1 to see how they affect Sheet2. Prime numbers give one kind of pattern, and composite numbers give a variation.
Extra Credit: Try different formulas to see what kinds of different patterns you can get. For example, in cell B2, edit the formula to say: =MOD(B1+A2+A1,Sheet1!$B$1). Copy that formula down and to the right, and choose odd numbers for your mod.
There you go. Knock yourself out. Have fun.
More tricks later.