Eigenvalues experiment

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Francisco Restivo (Author)

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WHAT IS IT?

Applies the matrix transformation to a set of unit vectors

HOW IT WORKS

There is one agent for each of the 128 unit vectors.

HOW TO USE IT

Choose the coefficients of the 2x2 matrix and press Go.

THINGS TO NOTICE

It´s a first step to understanding engelvalues and eigenvectors. You can use colours for an insight.

THINGS TO TRY

You can just press Go for a new experiment.

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CREDITS AND REFERENCES

Author: Francisco Restivo (frestivo@gmail.com).

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; Aims to emonstrate the eigenvectors of a 2x2 matrix

; Created by Francisco Restivo, frestivo@gmail.com

globals [tr det delta EV1 EV2 alpha x0 y0 x1 y1]

to go
 clear-all
 crt 128 ; 128 turtles, for 128 unit vectors
 set tr A11 + A22
 set det A11 * A22 - A12 * A21
 set delta tr * tr - 4 * det
 set EV1 0
 set EV2 0
 if delta >= 0 [
   set delta sqrt (delta)
   set EV1 (tr + delta) / 2
   set EV2 (tr - delta) / 2 ]
 ask turtles [
   pd
   set shape "circle"
   set size 0
   set color green + who / 28
   set alpha 360 * who / 128
   set x0 Scale * cos alpha
   set y0 Scale * sin alpha
   setxy x0 y0
   setxy 0 0
   set x1 A11 * x0 + A12 * y0
   set y1 A21 * x0 + A22 * y0
   setxy x1 y1 ]
end

There is only one version of this model, created over 7 years ago by Francisco Restivo.

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File	Type	Description	Last updated
Eigenvalues experiment.png	preview	Preview for 'Eigenvalues experiment'	over 7 years ago, by Francisco Restivo	Download

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