Math Is Fun Forum

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

integrating vector field + lorenz attractor

i got bored in school between my exams yesterday so wrote a little app that i compiled when i got home (since school doesnt have Flex2/Flash9alpha/FlashCS3)

it uses an RK4 integrator to integrate the vector field from the point whereever you clikc, if you click around enough places you start to get a proper picture of the field by its integrals:

requires flash player 9 obviously.

http://denvish.net/ulf/060607/41297_vecint.php

the vector field is given by:

where x is from -40 to 40, and y from -30 to 30

as a slight tangent:

http://denvish.net/ulf/060607/41650_lorenz.php

basicly the same thing, its integrating the lorenz attractor differential equations using an RK4 integrator again, projected into 2D, and then faded out so that it doesnt just become a big mess, colour faded to leave a dark grey silhouetter:

its running 3 integrations at once, with inital coordinates:

(0.01,0.01,0.01)
(0.01,0.01,0.01+1e-12)
(0.01,0.01,0.01-1e-12)

example of chaos, intial coordinates are only off by 1×10-¹² and over a few moments they become drasticly different integrals:

each frame it runs through 100 iterations per integral, with 100ms time steps, so each frame it runs through 10seconds

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George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: integrating vector field + lorenz attractor

Great!

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X'(y-Xβ)=0