A MAGIC BUBBLE BOX is releasing multicolored bubbles into the world at a breakneck pace
it can send out red bubbles, orange bubbles, blue bubbles - all the colors, really
best of all, people can control which and in what pattern colored bubbles are released from the box by giving it three simple instructions:
1. an ordered list of colors to be released
2. a total number of bubbles to be released until the box stops
3. a transition matrix that dictates for each color the probability distribution of colors that will follow it!
here's an example of a transition matrix for a two-color bubble box output:
R B
R .6 .4
B .5 .5
With these instructions, R will follow occurrences of R 60% of the time. 40% of the time, though, B will happen instead!
If the last bubble released was B, though, there's a 50% chance that R will be released next and a 50% chance that B will be released next!
If the transition matrix were
R B
R .5 .5
B .5 .5
Then every color would be equiprobable at any given moment. You can expect a sequence of bubbles of any length to be, on average, about 50% R and 50% B.
But a matrix like the first one I showed you might be a bit more complicated to understand. Furthermore, some matrices might involve many more than just two colors. In fact, most magic bubble box bros work with 8 colors at a time!
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