Note: this is a follow-on post from follow your dart.
In making games, I often want to randomly place objects inside a circle. I have always done this one of two ways, but I feel unsatisfied with both.
Method 1: Randomly pick a point surrounding square, and reject points which are not in the circle.
Polis: Fight for the Hegemony is a two-player asymmetrical territory-control board game. I'm usually cautious of territory control games, but Polis avoids most of my reservations. Firstly, it's strictly two player which means there is no kingmaking to contend with. Secondly, the game is exactly four rounds long so you don't have to play for aeons after a loss becomes evident. Its asymmetry is exciting, and the theme is strong.
Imagine throwing a dart at a dartboard such that it will hit any point on the dartboard uniformly randomly. What is the expected distance between the dart and the centre of the dartboard?
I don't like traditional four-sided dice. When you toss them, they just thud to the table without really rolling. Reading the number is also awkward. All in all, bad.
I have collected a couple of variant d4s which I find much more satisfying. On each, the number is clearly visible after rolling, and the dice actually roll on the table once you release them. I knocked together a couple of models in Blender to show the shapes I have:
For the purpose of filling out an in-development site with placeholder data, I decided to make a random name generator based on Markov chains. The goal was for it to create pronounceable and plausible names, but not necessarily real names.
First, a bit about Markov chains. If you have a set of "states", a Markov chain simply describes the probability of moving from any state to any other state. For example, imagine we have a mood lamp which changes colour every second according to the following Markov chain: