Freact

After seeing u/ipe3000 's post about his game INFINITO I was feeling intrigued but had no easy way to start playing. To that end I created a simple online demo where I (and you!) can try it out. The features are pretty minimal but you can play hotseat against a friend (or with yourself) and there is an AI opponent to play against. You can also select different board sizes. 8x8 is the default but it felt a bit intimidating for my first game so I made it possible to go all the way down to the trivia

The daily board on the app today has both Voyage and Island Folk. There were a couple times when I would have liked to choose which extra turn to take first, but I couldn't figure out how.

Sometimes I had played voyage during my turn, but then by the end of turn had collected enough favors and decided to redeem Island Folks. In this case, I'd like to take the Island Folks turn first since not being able to take a 3rd turn in a row means the Voyage turn would get skipped.

Another case that came up was after having played a Lich and Voyage during my turn and wanting to redeem Island Folks. In this case I'd like to take my Voyage turn first so that Lich skips it, then take my Island Folks tu

I've been thinking about the modular restriction method described on Wikipedia. The gist is that when searching for a non-trivial loop, one doesn't need to check certain residue classes of numbers that are known to decrease if all lower numbers have been checked. I think there's a way to rule out more residue classes than the simple method described on Wikipedia though. Ruling out all residues for any given modulus would be equivalent to proving there are no non-trivial loops, so reducing the number of possible cases is a way to make incremental progress towards that goal. Or, at the least it could make search for a counter example more efficient. Surely others have thought of this before an

This post is a follow up to my Collatz as Cellular Automata post. Since making it u/HappyPotato2 and others have helped me to explain some of the structures and to find more new and interesting patterns. If you haven't seen it yet you might want to go take a quick look to see how the automata works, but the gist is that the following images will contain the digits of some integer encoded into base 6 then collatz iterated row by row. The rule applied on each step is the same but it works in such a way that it automatically a

I've seen discussions here about focusing on only the odd values in a Collatz trajectory. This led me to some interesting thoughts I wanted to share. While some of this might be known, I hope it's still interesting!

When considering only the odd numbers, the structure of the Collatz tree changes significantly. In the standard Collatz tree, each node has a maximum of two predecessors. However, if we only consider the odd numbers, each node can be reached from an infinite number of predecessors.

Take the number 1, for instance. In the standard tree, it's only preceded by 2. But if we skip even numbers, the first odd number that leads directly to 1 is 5. If we follow the powers of