MAGIC SQUARES
and BI-FURCATION

by Raphiem

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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 bi-furcation?  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 | Mission-Ignition < missionignition@gmail.com > wrote:

Hi Greg

the formula at the url above is rather messy imho ..

i use a much simpler approach to bi-furcation 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(N-X)

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 bi-furcation.

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 11-12 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 | Mission-Ignition [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 | Mission-Ignition [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