Many "random number generators" in use today are defined algorithms, ... Stephen Wolfram used randomness tests on the output of Rule 30 to examine its potential for generating random numbers, though it was shown to have an effective key size far smaller than its actual size and to perform poorly on a chi-squared test.
It only takes a minute to sign up.I'm a little bit hesitant to ask this here, so please notice the tag.
I'll add the tags NKS (oh dear ..., but I think we'll survive) and cellular-automata, but leave you to remove the soft-question tag. Discuss the workings and policies of this site
As I understand it Mathematica in fact uses rule 30 to generate pseudorandom numbers by just reading down a single column: so what it's exploiting is not just that rule 30 behaves pseudorandomly but that columns look more or less like strings of independent uniform random bits. MathOverflow works best with JavaScript enabled
On the Design of LIL Tests for (Pseudo) Random Generators and Some Experimental Results, The #1 tool for creating Demonstrations and anything technical.Explore anything with the first computational knowledge engine.Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.Join the initiative for modernizing math education.Walk through homework problems step-by-step from beginning to end.
Also, I love the idea of the intuition tag.
946. Springer-VerlagYongge Wang 1999. =)I don't think this needs or deserves the "soft-question" tag you gave it. I heard that Feynman also had no intuition for it... which is not exactly hopeful. Stephen Wolfram was the first to suggest that Rule 30 could be used as a pseudo-random number generator (PRNG), and it was actually used as such in Wolfram’s Mathematica previous to version 5.0. LNCS 1716, Springer Verlag
In this case, you can call The next interesting part is the mess I made of the After that, we turn it into a three-argument function, taking the left, center, and right bits above it and returning the bit that we want.
If we label the four cells on which the rule is definedIn fact, the stronger property is true that rule 30 can be run leftwards. Rule 30 has no such properties.
However, I'm having a difficult time coming up with a convincing argument for why this would be true... beyond appealing to results from some kind of statistical 'tour de force' through all the elementary CAs using random initial conditions of varying length.I'd say more, but I really don't know much about cellular automata. In: Proc. Featured on Meta
My current method of adding some variance is to use a timer interrupt to seed the random number, by incrementing a number to be processed through an equation. Terry Ritter, "Randomness tests: a literature survey", webpage: Generate numbers sorted in ascending order or unsorted. There are many many references to the "Rule 30" CA - So my question is - beyond 'numerical phenomenology' is there an intuitive understanding why Rule 30 should behave in this random/pseudorandom manner?But I suspect that in general, the results of cellular automata are psuedorandom.
However, over the past century, a variety of tests of randomness have been proposed, especially in the context of games of chance and their rules. This description has 22 characters, and it can be efficiently constructed out of some basis sequences.Yongge Wang. 1989. Practice online or make a printable study sheet.Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram, S. "Statistical Mechanics of Cellular Automata."
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The maximum runs of white cells at generations 0, 1, 2, ... are 0, 0, 2, 1, 3, 1, 4, 2, 5, 3, 4, 4, 3, 2, ... (OEIS So one more function that will pad the width out to the correct length.With that, we’re just about there.
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rule 30 random number generator