Tiling

I took the following picture through the shop window of a business that is located just behind the physics lab.

This album is powered by BubbleShare - Add to my blog

I have been passing the tiling for weeks (probably much longer) but I recently started thinking about it. I have some questions for you to consider. I do not know the answers but I am interested to hear some of your thoughts.

How was this tile pattern generated?

One obvious answer is that someone said something like, "Ok. In the first row I want 4 whites, 1 gray, 2 whites, 1 blue, 3 whites, 1 gray, and 1 white. For the second row, I want 1 gray, ..."? Do you think this likely? Explain.

If the pattern was not created tile by tile, how was it done? A likely answer was using a computer program. But what type of instructions would the programmer give?

The name of the pattern is "Degradado Azul." Starting at the top and going from one row to the next, the number of blue tiles sometimes increases and sometimes decreases. Overall, though, the rows start without having almost any blue tiles and then end up, in the bottom rows, with all or nearly all tiles being blue. The number of blue tiles in each row must be increasing even though it sometimes decreases.

Do you see any other patterns? Could there be some sequence formula that a computer could use to generate the number of blue tiles in each row? Given the number of tiles, in what positions should the blue tiles be placed? How would that be decided?

Do you see any other patterns?

Do other questions occur to you?