Interesting Puzzle- how does this work?

1. Take an eight by eight grid (with 64 squares).
2. Fill it randomly with digits 1 through 8.
3. Now start at any number on the left most column.
4. Move that many spaces down your grid (going up to the top of the next column if you run out of space).
5. Whatever number you land on, take that many steps down the grid, moving to the top of the next column if you run out of space, and continue.
6. Continue this procedure, until you run out of room on the whole grid.
7. Mark the last spot you landed on.
8. Start again with a new number on the left most column of your grid. Redo the whole procedure.
9. Try again, starting with yet another number on the left most column of the grid. And again. And again.
10. What happened?

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