I recently posted a puzzle featuring a graphic of a stylized rosette. The rosette is nothing more than a rectangular spiral. See here for the original puzzle post. Here is a distillation of the graphic:
The spiral follows a clear pattern until we get near the center. And then I just sort of made it work to fill the space. What would have been the right thing to do to follow the pattern strictly?
Each "petal" is an Nx1 rectangle. Starting from the outside and spiraling inward, the pattern is very clear:
A petal of length N runs along the top
A petal of length N runs down the right side
A petal of length N-1 runs along the bottom
A petal of length N-1 runs up the left side
and so on...
It all works fine until we finish with the petals of length 2. Then what??
Some hypotheses:
- Perhaps I should have put a 1x1 petal in the "HERE?" block and considered it to be the bottom, and then put a 1x1 petal in the "GOES" block and considered it to be the left, and the remaining "WHAT" block should be kept as null because it cannot be filled in meaningfully.
- Perhaps it is simply not possible to continue the pattern past the point of N=2. After all, each new rectangle turns 90° from the previous rectangle. It is required to cover the one-block width of the previous rectangle plus some additional running length. Anything less than N=2 is just not long enough to do all that.
- Perhaps the pattern can be continued if we are willing to consider petals of length zero, i.e., 0x1 rectangles.
- Perhaps the center of the spiral is some sort of infinite singularity which cannot be depicted and I just should have blurred it out, like M.C. Escher did at the center of his drawing Print Gallery.