Last week, I invited my followers on Mathstodon, LinkedIn and Twitter to ascertain the logic behind this plot:

Before I reveal the answer and the winners, let me go through some honourable mentions in the responses:

• @bbarber_ suggested a projection of the positive orthant of the 4D lattice
• @springdot noted that doodles of feathers are what you draw when you want to be truthful
• @RobAnthony01 said it was a fractal where the central branch is repeated at about 80% of the original, which might be correct but I’m not going to measure
• @vatsasir said “bifurcation”. If anything, it’s a trifurcation.
• @phil_dubious tried to reconstruct the fractal, which is a good effort!
• @realityminus3 suggested “Plot: a person starts out telling three versions of the truth. Consequences ensue, disparate storylines entangle, the situation goes dark. Only one character emerges alive.” Love it.
• @jgfwstone reckoned it looked like a computer learning to ride a bike.

### The winners

• First response ((In future, I reserve the right to decide what constitutes a response. Going ‘first!!!’ isn’t going to get you a postcard.)): @MrAllanMaths, who suggested the Chinese Method for powers
• Most interesting response: On LinkedIn, Deborah Castle asked it it was a Fishikawa, which sent me searching. Lovely idea!
• Closest response: @shahlock suggested “some (wacky) visualization of (x+y+z)^n?”, which I think is morally quite close to the true answer.

All three will be getting postcards :-)

### The answer

In fact, the coordinates of the nodes of the tree represent the legs of primitive Pythagorean triples (plotted on a log scale). The edges are the links in this tree of triples – every primitive triple can be seen as the parent of three others. (There are several possible ways to do this; I picked the one that was simplest to code up.)

Wasn’t that fun? Let me know if you’d like to play again!