9/25/2023 0 Comments Conways game of life self assemblyLet’s use this program to compute fib(7). In this program’s case, to compute fib(x) for some value of x, we compute n = 78 * 5^(x - 1). When it’s provided by the user, there is sometimes a need to prepare n to make it usable. That value is sometimes a constant, and sometimes provided by the user. 11Īll FRACTRAN programs also start with an initial value for n. for the first fraction f in the list for which nf is an integer, replace n by nf.The program is run by updating the integer n as follows: Gotinath, “Open Problems in Communication & Computation” 10 our first fractran programĪs Wikipedia notes, a FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input n. Perhaps the most entertaining of all the contributions is Conway’s fascinating article on FRACTRAN, a strange collection of numbers, which when operated on in a simple way, yield all possible computations. California.įRACTRAN itself was not an important open problem in the field, but as the editors noted: In 1987, Conway contributed FRACTRAN: A SIMPLE UNIVERSAL PROGRAMMING LANGUAGE FOR ARITHMETIC to a special workshop on problems in communication and computation conducted in the summers of 19 in Morristown, New Jersey, and the summer of 1986 in Palo Alto. norman wildberger’s lecture on the collatz conjectureĪ fragment of John Horton Conway’s paper on FRACTRAN.conway’s “fractran: a ridiculous logical language” lecture.fractran and marvellous minsky machines.encoding state with prime factorization.Gödel Numbering and Masterful Minsky Machines an algorithm to derive a marvellous minsky machine from any magnificent minsky machine.implementing magnificent minsky machines.the magnificent minsky multiplication machine.a notation for magnificent minsky machines.writing a fractran-based fibonacci function in javascript.“Books” © Stewart Butterfield, 2012, Some Rights Reserved The subject of numbers and representation leads us to FRACTRAN. Like the Game of Life, Surreal Numbers keep popping up unexpectedly, reigniting my interest in how the way we represent data, affords or hinders working with that data. That led me to Conway’s On Numbers and Games, and via parallel paths, to Surreal Numbers. I spotted Games of Strategy: Theory and Applications in a library and picked it up, thinking it would help my Backgammon. Some years ago, I read William Poundstone’s The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge, and it literally blew my mind. I went on to rediscover Conway’s Game of Life several times in my life. 5 6 7Īn infinitely scrolling implementation of Conway’s Game of Life I don’t recall playing with it much: There was a lot going on, and it’s entirely possible that I was too busy falling in love with Raymond Smullyan to have curiosity left over for John Conway. One of the things we talked about in “Whodunnit” was Conway’s Game of Life. It turned out to be a half-day exercise in puzzles and games, and I was hooked. ![]() The “students” self-selected electives, and I picked one called Whodunnit. My mother had sent me to a day camp for gifted kids once, and it was organized like a university. As I described in The Eight Queens Problem… and Raganwald’s Unexpected Nostalgia: One of the finest examples of that skill is the programming language FRACTRAN, the subject of this essay.Ĭonway touched my own life from early days. I celebrate his accomplishments, I celebrate his curiosity, and I celebrate his skill at making important topics in mathematics engaging and interesting. Like so very, very many, I mourn Conway’s passing, and yet I also celebrate his life. On April 11, 2020, he succumbed to the disease. On April 8, 2020, John Horton Conway developed symptoms of COVID-19. RAGANWALD.COM Remembering John Conway's FRACTRAN, a ridiculous, yet surprisingly deep language
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