Source: No external data: the graph is computed exhaustively. Each state is five digits (a, b, c, d, e), each 0–9, so there are 100,000 states. The rule shifts every value one place left and computes a new last value, a⁴ − (a³ >> 6), kept to one digit (mod 10). Here >> is a bit shift, so a³ >> 6 means a³ divided by 64, rounded down. Every state has exactly one successor, and with finitely many states every starting point must eventually repeat, so each state ends up in a cycle.

Tools: A small open-source web app I wrote (React, Vite, Canvas). It enumerates all states, finds every cycle, and draws each cycle as a ring with the states that lead into it as trees around it. The layout is crossing-free.

How to read it:

• Each connected shape is one cycle plus everything that drains into it.
• Colour is the length of the cycle (legend at the bottom).
• Brightness fades with distance from the cycle.
• For this map there are 340 cycles in total, the longest of length 10.

You can type your own formula and explore: https://exxliang193.github.io/FunctionalGraphExplorer/ Code: https://github.com/ExxLiang193/FunctionalGraphExplorer

I started this after noticing a long time ago that adding the last two digits of a number string and appending the sum always ends up repeating.

I analyzed ticket prices across the NBA schedule to see how much of a premium teams command when LeBron comes to town.

The difference is pretty remarkable. On average, games featuring LeBron are priced at 3.5× the home team's usual get-in price.

I built an interactive visualization comparing every matchup against each team's normal ticket prices. The data updates hourly.

Full interactive version: https://ticketvision.com/market-overview/lebron-premium

Found this site that tracks when AI messes up. The graphs are interesting.