Is it impossible to digitally create a randomly evolving pattern?

Question

I was recently playing an old game on my computer, "The Incredible Machine". It consists of placing different objects which interact with each other to solve a puzzle, which is like a "Rube Goldberg machine".

I was trying to create a puzzle that basically took minutes to resolve itself, where bouncing balls would make bombs explode, breaking walls and opening new sections where the balls would propagate and open more sections. I was surprised to see the same kind of behavior seen when playing the "life game" where a set of dots driven by a simple mathematical formula propagate themselves on a grid. Many times playing "TIM", the animation either finished in a "stop" or in an "infinite loop", and no matter how random the pattern may seem, it always evolved and died the same way if the initial factors were identical.

Does this mean that it is impossible to digitally recreate a situation of chaos? Are these digital restrictions limiting our technological development potential?

Answer 1

Chaos is not random. What the mathematicians call chaos is systems with "sensitive dependence on initial conditions". This means that a small change in the seed number can result in a large difference in the outcome. However, chaotic systems are deterministic. That means that if you start with a particular number, you will always get the same pattern.

As far as certain starting points going to a dead end or an infinite loop, it is typical of chaotic systems that there are some regions of input conditions that lead to a stable result, and others that run away or dead end. Mapping of these regions can produce fractal patterns such as the Mandelbrot set.

You cannot generate truly random behavior with a computer program. Many computer programs use the exact time to compute a seed number, thus assuring that the numbers don't repeat. But to generate truly random numbers, you need some sort of physically random process that you can measure.

Answer 2

In a computer sense you have to be very careful what you mean by random.

A random sequence of numbers is one in which the probability of each number occuring next in the sequence is the same. In other words, a probability diagram would be a straight line.

You can derive algorithms that produce such sequences. However, given the same seed they will produce the same sequence each time. The sequence will be statistically random, but deterministic.

Getting something truly random out of a computer is MUCH harder.

Answer 3

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