GC SF Sp WH BV YL BT CP SA CB CC Back to puzzle

Cascade Bay

Snowy Flow

by Jesse Morris
Answer: THERAPEUTIC BATH

This puzzle has a bunch of clearly recursive snowflake shapes, in two signs. The first sign labels each shape as a letter, establishing that the shapes form a cipher. However, none of the letters used in the first sign are present in the second, so solvers will need to crack the encoding.

Astute solvers may notice that L and S snowflakes are mirror images of each other, as are F and Y. Those pairs of letters also happen to be binary complements of each other.

The snowflakes encode binary information representing letters. Each snowflake has 5 different asymmetric shapes (4 different sized holes, plus the overall outline of the snowflake). Each could be seen to spiral in one of two directions. Counterclockwise is a 0, clockwise is a 1. The larger shapes represent more significant bits.

the letter H

Solvers can determine the binary codes for the second sign to find answer, THERAPEUTIC BATH.

detailed hexagon
T
detailed hexagon
H
detailed hexagon
E
detailed hexagon
R
detailed hexagon
A
detailed hexagon
P
detailed hexagon
E
detailed hexagon
U
detailed hexagon
T
detailed hexagon
I
detailed hexagon
C
detailed hexagon
B
detailed hexagon
A
detailed hexagon
T
detailed hexagon
H

Construction Notes

The snowflakes were constructed by assembling hexagons into bigger hexagons, and those into bigger hexagons, and so on.

There is only one way to assemble 7 hexagons into a larger hexagon (or 6 hexagons into a ring), but there two ways to assemble 7 of these metahexagons into a metametahexagon

iteration step 1

Whichever path we choose for that layer, adding another layer introduces another choice.

iteration step 2

And so on: 7 level n metahexagons can always be arranged into a level n+1 metahexagon in two different ways.

iteration step 3

We chose to drop the middle hexagon at each step—so instead of solid hexagons and metahexagons, these formed hexagonal rings and metahexagonal snowflakes. This preserves the shapes of each of the layers building up to the final product. Though the outlines would still be distinct and information is not actually lost, preserving the holes makes the extraction process much easier.

Whether clockwise is 1 or 0 or even which construction you consider "clockwise" is arbitrary, so example text guides the way.

Fun fact: This puzzle depicts 29 snowflakes. Counting the middles, each one is 76 hexagons, for a total of around 3.4 million hexagons. My vector editing software (Affinity Design) was not thrilled with the situation, though it ultimately succeeded, with what is, arguably, a pathological use case.

Thanks to Brent Holman and Larry Hosken for helping out on this puzzle.