42 examples of Composite Mulanept Patterns
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42 examples of Composite Mulanept Patterns
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03/11/2014, 06:13 AM
42cmps.pdf (Size: 779.88 KB / Downloads: 848)
the 42 CMPs or Composite Mulanept Patterns are a small selection of about 140,000 patterns that can fit comfortably on your laptop screen  they could be composite mulanept patterns or more generally, functional type shifting patterns  
03/12/2014, 11:52 PM
are really fascinated by these things ...but
I was never able to understand how they work and what they are... I read your first two paper two times! but I cant get them. I just have the feeling that is a way to "draw" very big numbers , right? Can you maybe link me your easier explaination about them or explian your work in very easy words for "slow" people like me? MSE MphLee Mother Law \((\sigma+1)0=\sigma (\sigma+1)\) S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
03/13/2014, 05:15 AM
sure thing MphLee
regarding: "I just have the feeling that is a way to "draw" very big numbers , right?"  yes that's a good summary of the idea They are strange things because they are about information pathways that exist in big and complicated numbers These numbers have a main starting position and ending position, and to notice these positions you need first to recognise the folding pattern being used. The "default" folding pattern I use is start at bottom right then Fold to the Left, then Fold in the Up direction This is Fold_LU and there are 8 possible folding patterns. Noticing the way the folding pattern actually works has a subtle  aspect, the first fold up looks as thoughit is folding down but this is only to obtain the so called seed value to start the upwards direction. Likewise, the next Fold Left requires a brief shift to the Right to pick up the next seed value before pushing to the Left direction, and so on and so forth. You can imagine the process as being one of "transference". You study the symbol representation of the formulae and notice the symbols or glyphs in the formulae have a regular pattern, again relative to a folding pattern. 
03/13/2014, 06:23 AM
MphLee
Another thing to notice is about "ordertype" ... ordertype4 corresponds with hyper4, and ordertype5 with hyper5 and so on. But the thing is there are hyperoperations and the between stages of iterations of a hyperoperation before reaching the successive hyperoperation that "plucks up" a new seedvalue. The non standard tiling patterns are representations for pure hyperoperations (pure noptiles), iterations of pure hyperoperations (compositions of pure noptiles), and also any composition of hyperoperations using any well defined bracketing pattern and any ordering of hyperoperations as can be seen from the examples. The other useful thing to recognise is to observe the Unique Initial seed value and the Unique Outer seed value of each of the pure noptiles, no matter what the ordertype is. Assuming the folding pattern used is Fold_LU, we notice The Unique Initial Seed Value, ISV, is always at the bottom right position of a pure noptile and is starting an ordertype4 or ordertype5 subcomponent of the noptile. However, the Unique Outer Seed Value, OSV, is always alternating between the Right mid region position and the Bottom mid region position, so with hyper4, the OSV is on the right; hyper5 the OSV is at the bottom; hyper6 the OSV is at the right; hyper7 the OSV is at the bottom... And the areas of the "minimal enclosing rectangles" for the pure noptiles grow approximately exponentially in area. The Initial seed goes with the hyperbase and the Outer seed goes with the hyperexponent. This is a regular feature, and allows the compositions to be well defined, although when pipelines are needed, they are used to join component noptiles together from one of the Non-Unique pure noptile attachment squares and either is attached to, or pipelined to, the ISV or OSV of another noptile, as appropriate according to the subexpression of the formulae expression. hope this makes it clearer. this is according to interpreting the patterns as composite mulanept patterns (see the other papers for more explanations and examples) they can also be seen (a bit more) generally as functional type shifting patterns with other interpretations, such as plus or times instead of exponentiation as the constituent operation, or standard positional notation with fixed arbitrary base(n), but I think only a proper subset of the patterns are valid with the SPN assumption... to avoid the yucky issue of redefining the finite base to nonsensical values.
03/13/2014, 08:42 AM
Thanks!, I'll think more about it. I'll ask you if I don't get something.
 MSE MphLee Mother Law \((\sigma+1)0=\sigma (\sigma+1)\) S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
by the way
March 14 is international pi day ,.,.,.  http://www.piday.org/ don't forget tau though ,.,.,.  http://tauday.com/ from The Tau Manifesto http://tauday.com/tau-manifesto "The Tau Manifesto first launched on Tau Day: June 28 ( 6/28 ), 2010. Tau Day is a time to celebrate and rejoice in all things mathematical." ~,'~',~',~,'~,'~',~',~,'~,'~',~',~,'~,'~',~',~,'~,'~',~',~,'~',~
for those unfamiliar with these Zen pattern numbers of the third realm or region, floating beyond the large GIMPS Mersenne prime numbers, I thought I'd mention some of my inspiration and influences; or ideas that seem vaguely relevant
it's easy to find weblinks for these people and websites an interesting visualisation of one billion is available Visualisation of powers of ten from one to 1 billion http://en.wikipedia.org/wiki/1000000000_(number) Robert Munafo classes of natural numbers aka counting numbers, positive integers Reuben Goodstein names for hyperoperations, Goodstein's theorem John Horton Conway Conway chained arrow recurrence relation, the fourth realm, and heaps of wide ranging math ideas Donald E Knuth simple but good notation for hyperoperations concrete math and art of computer programming books Ronald Graham Graham's number Wolfram Research cellular automata, NKS, Demonstrations project and Wolframalpha Piet Hein superegg M C Escher amazing patterns and art Edward R Tufte visual display of quantitative information Andrzej Grzegorczyk another perspective on the third realm or region the Fast Growing Hierarchy and Grzegorczyk Hierarchy Georges Perec whose contributions to Oulipo were inspiring I had to follow the ideas from Oulipo to think creatively enough about the natural numbers, when in math mode, I was usually trying to think creatively about basic things Patrick Gunkel whose contributions to innovative thinking were inspiring other inspirational people Benoit Mandelbrot Mandelbrot set (1979) David Madore tree pictures of transfinite ordinals, interesting visualisations but complicated to understand Jonathan Bowers polyhedra, polychora and fourth realm ingenuity ( Bowers arrays ) gmalivuk, deedlit, wardaft and heaps of others ......... xkcd forum, My number is bigger game iteror another approach to the name big numbers game I used to be interested in reading papers on these websites Calresco and CCSR and Principia Cybernetica complexity studies, artificial life ... Tim Berners Lee the worldwide web is 25 years old or young Quickfur on Eretrandre who sort of seemed to be thinking along a similar path to me and of course the wonderful Eretrandre people Henryk Trappman, Gottfried Helms, Dmitrii Kouznetsov, and others who invented or discovered the beautiful tetration fractal pictures and the many deep mathematics ideas on Eretrandre and of course many others I forget but who also influenced me or others who I remember, but if I mentioned them all there would still be others I missed but should have included 
06/25/2014, 12:07 PM
Lots of numerical examples related to these patterns
can be found in the Googology Wiki the large number encyclopedia* there are many examples in the Photos section of the Wiki *maintained by Jonathan Bowers and Sbiis Saibian http://googology.wikia.com/wiki/Googology_Wiki they are pretty and entertaining to look at ...  |
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