Animation of Matrix outputs
- To: mathgroup at smc.vnet.net
- Subject: [mg43120] Animation of Matrix outputs
- From: gauer at ras.sk.ca
- Date: Wed, 13 Aug 2003 07:49:52 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
<see Re: [mg41837] Re: Multiplying permutations for a similar study>
I am investigating lists of the form (k fixed) in my spare time:
For[
n=0, n<k, {a, b, c, d, ..., k}.Print[MatrixPower[A,k]//MatrixForm, ++n]
]
Suppose that each letter of the alphabet represents a different grayscale
or colour, perhaps coloured by its element order within the group (lighter
colours correspond to smaller orders, perhaps).
Note that it is easy to pick a group table now by:
taking the ith output and assigning it to the ith row a kxk matrix for
each i, and seeing if any two different matrices are isomorphic to each
other (for some permutation in question).
First question is: how can I generate the set of all non-isomporphic
groups of order k (let's say that k is max of around 500)? Can I use any
of the njas sequences to read them in, and then create them, or are they
already built in to Mathematica? Which sequence numbers are best to look
up to get an easy form to read into Mathematica?
Second question is more of an animate problem, but for TextOutPut, rather
than Graphics:
For[
n=0, n<k, Print[MatrixPower[A,k]//MatrixForm, ++n]
]
where A is a matrix with elements of 1's and 0's (max of one 1/row and one
1/column) and 0<i<=k such that k={least value of MatrixPower[A,i]=A}.
Next step is: to animate the Powers of the Matrices being outputted,
similar to how one could produce a graphic animation.
So I Plot[somefunct,PlotLabel->{kth_Printout}] k times with a for loop and
try to animate the output (and have tried MakeAnimation as well). I've
also tried calling the output as a Graphics List, but doesn't seem to rid
the error returned. However, when trying to animate, the output seems to
think that the output is still nothing but a series of k //MatrixForm
outputs, and won't understand it as being 30 separate labels of a graphic.
Question is: how to get the MatrixForm output animated, if possible (yes,
I know that in version 3 that you have to turn it on in the Menu after
selecting the output cells)? I couldn't care less about what the somefunct
is - it may as well have colour = white.
Assigning a lattice of black and white cells is something I thought of,
later to addd in functionality of having an element represent a colour,
but for these purposes, if I can generate just a black and white flashing
lattice, I'd be happy.
Thanks in advance. I'm not in front of my Mathematica terminal right now,
so apologies for the pseudocode. version is 3.0.
-- Kai G. Gauer, B. Sc. (Mathematics) --
Alumnus, Luther College, University of Regina
Royal Astronomy Society of Canada Regina Centre
www.rasc.ca www.reginachessclub.com www.ras.sk.ca
-- Regina Cathedral Centre Chess Club --