Fixed Points

Author

Matvey Soloviev (ms900)

Description

This puzzle is very similar to its singular predecessor, but bears some additional challenge in that, as the title suggests, there are now multiple fixed points (and, accordingly, each code number is no longer unique, as it could denote distance to either of them) - and that the function is now only given as a plotted graph as opposed to a nice letter-mapping widget. It is perfectly possible to go down the route of simply tabulating this function and performing the necessary calculations by hand - or even feed the table into the JavaScript code from the previous puzzle! - but a somewhat more entertaining way, in the author's opinion, is to simply do some old-fashioned graphical reasoning.

A simple diagonal line quickly reveals the location of the two fixed points:

Iterating the function graphically is only slightly more involved, and can be executed using rulers and pencils, or perhaps the graphics processing software of your choice, like so:

Writing the two alternatives, i.e. the letters which take the given number of steps to reach one of the fixed points, for each position below each other, the solution word will stick out quickly.

Solution

computability

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