Adding WiFi to the micro:bit is fairly easy using the low-cost ESP8266 ESP-01, which connects via the serial port and makes use of AT style commands to control the device as if it was a WiFi modem.
In addition to an ESP8266, you also need a power supply capable of running it.
You can use AT commands to set the device into client mode and connect to a WiFi network.
While it is possible to use ad-hoc protocols, there are advantages in using TCP, HTTP and HTML so that other devices can work with the micro:bit.
The micro:bit can use client mode to download data from web servers.
It can also emulate a server to deliver data to any web browser or HTML-using client.
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The thing about the BusyBeaver function is that it is very easy to understand, but very difficult to compute. We now know its value up to 5, which isn't much progress for more than 50 years work.