Absolutes (part 1)

Step 1: Have Excel punch out a bunch of random numbers between zero and one. Each number is each fifteen digits long.

Step 2: Have each cell in the adjacent column complete this calculation: determine the absolute value of the difference between the cell in previous column but the same row and cell in previous column and previous row.



Step three: Let the top cell wrap around to the bottom.




Step 4: Create a bunch of iterations by copying the formula into more columns.



Step 5. More! More! More! Also, color them: red: close to one, blue: close to zero. Also, shrink the cells (Though it says "1" and "0", the number is a string of digits, there's just not room to display it).




Step 6. Refresh, look for patterns :D



Here's a bigger version:





Here's a much bigger version:




And a much much bigger version:



It seems that after a long enough time there's a sort of blue-ing out that always happens. All the numbers get close to zero and the nice red fractal-like triangles fade away.

Here's where I did something sneaky... I told the computer to adjust the red vs. blue proportions so each column has the same average color value. In other words, I normalized the colors. If a column has too much blue it reddens up to match its neighbors. The effect of this is to allow us to see very subtle differences between cell values.

(See the rest in part 2)