MAGIC SQUARES
and BIFURCATION
by Raphiem
From: Greg Ehmka [mailto: gregehmka@gmail.com ]
Hey Raphiem,
The torsion wave stuff is fabulous, direct connection to some math work I'm into. ...and a short question. What definition are you currently using for bifurcation? One like the heavy math approach, for example here:
http://www.sosmath.com/diffeq/first/bifurcation/bifurcation.html
Or one of your own?
thanks, love and peace ... greg
On 4/13/07, Raphiem  MissionIgnition < missionignition@gmail.com > wrote:
Hi Greg
the formula at the url above is rather messy imho ..
i use a much simpler approach to bifurcation more designed around my heavy use of magic squares
simply it is X=AX
where X= population
and A = fertility
but then i extend it for use with magic squares in what i call "environment"
i.e.
X= AX(NX)
where N = environment
when used musically for shifts in octaves i.e. period doubling you find the bifurcation ratios actually are equal to the Feigenbaum constant of 4.6692016
this is something you should also look into i.e. the Feigenbaum constant as related to bifurcation.
i hope i haven't lost you
Peace
R.
From: Greg Ehmka [mailto: gregehmka@gmail.com ]
Sent: Saturday, 14 April 2007 4:46 AM
No, I'm right with you.
The url is evolving the system parametrically over t = time. And if I have it right, you are using the iterative approach meaning "last output becomes next input" which evolves the system "from state to state," kind of ignoring time proper and is more interesting for fractals, generating attractors etc. plus easier since derivatives aren't used. The logistics equation seems quite useful in both approaches.
The two approaches together gave me something I was trying to understand about where the quadratic equation solutions become complex.
I was reading some chaos stuff 1112 years ago and came across the Feigenbaum constant but NOW I get what the ratio actually means. thanks.
Also I've never done anything with magic squares, do you have a fav site for me to catch up on them quickly...?
From: Raphiem  MissionIgnition [mailto:missionignition@gmail.com]
Sent: Thursday, 19 April 2007 1:37 PM
Hi Greg
wow ... it's good you understand it all ... yes i use the stepping / iterative approach as you highlighted as am usually dealing with number of steps taken to reach a balance rather than a time approach and for me is more conducive to computer programming ... and also i can use it then to insert into my magic squares ... which is a whole different kettle of fish all together ...
there are many sights that talk about maths apporach to magic squares but am not sure if you are aware magic squares/cubes are harmonic patterns of balance which many mathematicians are not aware of
here is an example of magic square harmonic pattern
first image is just the magic square of 8x8
all rows and columns and diagonals add up to a balanced 260 ...
64, 2, 3, 61, 60, 6, 7, 57
9, 55, 54, 12, 13, 51, 50, 16
17, 47, 46, 20, 21, 43, 42, 24
40, 26, 27, 37, 36, 30, 31, 33
32, 34, 35, 29, 28, 38, 39, 25
41, 23, 22, 44, 45, 19, 18, 48
49, 15, 14, 52, 53, 11, 10, 56
8, 58, 59, 5 , 4 ,62, 63, 1
now watch when i translate it to a picture/pattern
have you seen these before??
take care
R.
From: Greg Ehmka [mailto:gregehmka@gmail.com]
Sent: Friday, 20 April 2007 2:58 PM
Hey Raphiem,
No I've not seen the pattern before. Very interesting. It seems you are simply drawing a line to each integer in sequence and as simple as that is, I don't find it anywhere with a preliminary image search. So cool.
Is the significance that the harmonic and balanced qualities you refer to create symetry and/or those two apparent "focus points?" At that resolution I counted 14 lines going through the points. Is that correct?
peace... g
From: Raphiem  MissionIgnition [mailto:missionignition@gmail.com]
Sent: Monday, 23 April 2007 11:59 PM
Hi Greg
the magic square 8x8 pattern is one of many ..
now imagine
you have 9 people or 9 fileservers... each with different strengths (processing power)...
you want to group them in three's but want to make sure when combined they are all equal groups .i.e. "load balanced" a term we use in IT/computing when there are more than one device doing the work in parallel rather than serial.
i.e. one group is not stronger or weaker than the other ..
how would you do it ..
well to answer .. use a 3x3 magic square
8, 1, 6
3, 5, 7
4, 9, 2
all rows = diagonals = columns ... sum to 15 ... so you can say the square is harmony!!
so now rate each of your 9 people or FileServers by strength ... starting with 1 for the weakest to 9 for the strongest
then group them anyway you like as per below ...
any three rows
or three columns
diagonal not useful as there is only two diagonals
but i think you get the idea of application here
to be expanded / continued
Raphiem
