- Isaac Asimov, I, Robot
Can Simple Rules Explain Creation?
In this video - "Computation and the Fundamental Theory of Physics", Stephen Wolfram postulates that large structures, even the universe, can be derived from simple rules. Wolfram demonstrates this with a set of simple instructions for drawing a lines of white and black squares across a computer screen. Whether a square is white or black is determined by three values, the value in the square immediately above the one to be drawn and the ones before and after it.
Considering instructions as a binary numbers, with white being “0” and black being “1”, there are 8 [ 23 ] combinations. These combinations can be arranged in 256  ways — representing the 256 Rules.
Wolfram uses a number of examples that demonstrate, while most of the rules will result in repeating patterns, some will result in complex patterns. Most notably, Rule 30.
In generating these patterns he ‘seeds’ the program with a 1 (a black square) or a random number in the center of the first line.
Is ‘Seeding’ Necessary?
‘Seeding’ the program implies the initial conditions of a universe must already exist before the rules can be applied. While this does generate some interesting observations, can this be taken one step further. Can a complex pattern be generated from simple rules without ‘seeding’ the program?
It turns out it can.
When converted to a binary number, all odd number Rules end with a ‘1’ — drawing a square when the instruction is ‘000’. Therefore there will always be at least one black square for every odd numbered Rule. Most of the resulting patterns are fairly benign — alternating black and white lines or completely black screens. However, there was one, Rule 169, that shows some degree of increasing complexity.
If we accept Wolfram’s proposal, it is not hard to imagine a situation where just the existence of a simple set of instructions and rules implementing those instructions results in the creation of a universe. It is not necessary to ‘seed’ the universe for it to come in to existence. — The ultimate example of a ‘self fulfilling prophecy’.
- For Rule 73, the video stops at 300 iterations, the demonstration goes to 500 iterations. A change in the output starts after line 300.
- Rule 110 runs for 3,000 iterations which pushes the output to the right.
- I didn’t add the ability for ‘seeding’ a random image so Rule 184 is not fully enabled.
Running the Program:
- Enter a Rule in the input box.
- Click ‘Show Pattern’ to display that pattern
- Click ‘Start’ to start showing all the patterns starting at the value entered in the input box.
- Click ‘Stop/Pause’ to stop the output
- To ‘Clear’ the input you must first ‘Stop’ the output.
Enter a Rule Number between 0 and 255: = Binary 00000000
Start with: 1 0
Show all patterns:
- — Due to timing issues with the program when stopping the output, the Rule number displayed in the input box may be one larger than Rule shown in the display.
- — I resolved the issue of what happens at the first and last positions, which don’t fit the Rule structure, [No elements before or after.], by padding the ends of the output with ‘0’
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