Simple programs that produce randomness, Small universes of complexity

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	• A New Kind of Science Stephen Wolfram Wolfram Media, 2002 - 1192 pages average customer review:based on 331 reviews view larger image
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Simple programs that produce randomness, Small universes of complexity

Computer automata will provide scientific advances remove 300 years of fragmented thinking. CA's are simple mathematical formulas that create repeating pattern over long periods of time. Computer Automata seem unpredictable and random at a glance, but they end up too be highly predictable patterns and these simply programs build patterns representative or identifiable as individual universes of complexity; where these simple forms or formulas evolving into complex forms and manifested through predictable cycles of growth and adapting over time.

CA are similar too fractals in their algorithms follow simple programs. The programs can be recursive or a tree structure. CA application demostrate structures familar in nature and physics, simulating differential equations, and observing randomness of numbers is very profound. Each of the CA provided in the book are simply illustrated. For example, the author demonstrates binary patterns for prime numbers, taylor series, and linear algebra using a simple CA. Other CA applications demostrate more complex mathematical phenomena using simple programs. The CA for model thermodynamics seemed similar to the photograph of an actual thermodynamic pattern.

CA are intriquing. Its interesting to see the patterns that a CA can produce. The process of creating a CA seems intuitive. One observes a pattern, builds a simple CA to model his observation, and tests the output.

The concepts in the book are simply illustrated. The amount of content is comprehensive, yet each chapter offers interesting patterns and examples of CA application. CAs can be modeled in 3D providing complex spatial structures to similar pattern.

CA simplicity will sometimes yield complex behavior and patterns using small programs. Complex programs will sometimes produce simple patterns. CA is capable of modeling complexity. CA are used to model physical systems, chemical systems, and biological patterns of nature.

Lets look at the randomness of numbers Rule 30 and Rule 110, I will illustrate rule 110. In a simple CA, each cell has two possible states, black or white and each cell has eight neighbor cells touching. The next color in a cell depends on the color of its neighbors. Rule 110, 111->0,110->1,101->1,100->0,011->1,010->1,000->0 so, if 3 adjacent cells have a left cell that is on, the middle and right cell off, then the middle on the next line will be off (following the pattern 100->0 On Off Off produces off on the next line. The results are 1, 11, 111,1101,11001,110001.

Rule 30: 111->0, 110->0, 101->0, 100->1, 011->1, 010->1, 001->1, 000->0 Rule 30 says that if three adjacent cells in the CA have the pattern 100 (left cell is on, middle and right cells are off), then the middle cell on the next line will become 1 (on). The rule 110 CA says the opposite for that particular case. Rule 30 seems to pass the test for randomness. The input pattern 1101011010 will a CA Rule 30 pattern of 110011100110, where Rule 110 will produce from the same input the pattern 111111111100.

Rule 90: 111->1, 110->1, 101->0, 100->1, 011->1, 010->0, 001->1, 000->0. The CA (XORed) creates a Sierpinshi sieve: starting with the top value being 1, the value on the next row between the addition of its two adjacent parent values: Row 1=[1], Row 2=[1,1],Row 3=[1,2,1], Row 4= [1,3,3,1], Row 5=[1,4,6,4,1] The odd numbers are dark and the even numbers are light.

Rule 110 demonstrates infinite non repeating patterns generated by a simple discrete algorithm. Rule 110 suggest complexity is a continum. Complexity does not create order. However, the study of complex patterns is intriguing. However, increasing the complexity does not mean increasing the order.

Discrete functions can be programmed in software. Information demonstrated in Physics, math, and biology can be digitally represented as discrete functions.

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Thorough Treatment of Complex Systems

Often, scientists observe nature, then work on equations to model the observed phenomena.

Stephen Wolfram writes in A New Kind of Science (NKS) that this approach, while still having its place, needs an update because of its tendency to ignore complex phenomeno or cast complex phenomena as curious special cases.

Wolfram posits in NKS that many irreducible complex problems from nature arise not from the sheer amount of information present, but rather the prevalance of universality (as embodied in Turing machines and Wolfram's favorite, cellular automata).

Because computation keeps getting faster and cheaper, Wolfram professes that the most direct way to understand many complex natural phenomena is to pull up findings from one's study of computational simulations based on simple programs.

This is interesting because it implies that researchers ought to spend less energy massaging equations, and instead spend more time memorizing the behavior of simple programs.

The main NKS text is not as concise as it could be, and it lacks formal citations. Additionally, Wolfram's exhuberance for his own research comes off as hubris in many places throughout the main text.

This is unfortunate because the author gets marginalized at the expense of a very practical, thorough treatment of complex systems.

For any matter, the main text is a good read for laymen, and also a proper segue for scientists interested in the much more more clearly thought out appendix.

For people who like to study the interplay between physics and computer science, NKS is a worthwhile read because it provides insights into the techniques and reasoning employed by one of the most brilliant physicists who also continues to play a pivotal role in the advance of symbolic computation.

For the practical implications of NKS, the terrific appendix, and a chance to understand Wolfram's line of reasoning as a pioneer in complex systems research, I recommend NKS to anyone wanting to gain a fuller understanding of complex systems.

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A Mega Book

A mega book. Some fundamental thinking for the 21st century. Absolutely recommended for anyone who wants to understand how the world works, and gain insight into how man should design in the future. A daunting 'read'. More of a study. But immense depth and insight.

reviews: 1, 2, 3, page 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

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