## Patterns from RandomnessMay 18, 2017 The worldwide gambling industry has a market size of more than half a trillion dollars, with the US share being about $50 billion. It's expected to reach a trillion dollars within the next five years, fueled in part by online gambling opportunities. Since I'm a scientist well versed in statistics, I never gamble. One engineer I know does buy lottery tickets, two at a time, since he says buying the second one doubles his chance of winning. Sports betting is exciting to many people, as the popularity of office basketball pools attest, but much gambling is built on the concept of randomness, as in dice throws, roulette spins, and slot machine pulls. These are example of physical randomness; and, in electronic versions of these, computer-generated randomness. Computer-generated randomness was problematic in the past, since computer-generated pseudorandom numbers are produced by algorithms. As computer pioneer, John von Neumann, said"Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."
π/4.
• Draw an equilateral triangle.The chaos game construction is an additive process, rather than the subtractive process described above. A random point is chosen in a plane containing an equilateral triangle, a die is rolled to select one of the vertices of the triangle, and another point is drawn halfway between the first point and the vertex. The process is repeated using the last point. I wrote a generating program in C (source code here), and the results of 50,000 iterations are shown in the following figure.
## References:- Chaos Game, Numberphile YouTube video by Brady Haran, April 27, 2017.
- Wikipedia page on the chaos game. The simulation program can be simply modified to produce such different shapes.
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