25b5d902-c3ad-497a-841a-7a5e7021805e 10 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Lorentz attractor Rkadapt project

u Y D 8 Y 1 el * - 8 Y 2 el * + 30 Y 1 el * Y 1 el + Y 1 el Y 3 el * - Y 1 el Y 2 el * 83 / Y 3 el * - 31 mat :

t0 0 : t1 10 : N 1000 : 31 line

vinit 1 - 0131 mat :

s vinit t0 t1 N u Y D Rkadapt :

Lorentz s 2 col s 3 col augment : θ rot θ cos θ sin - θ sin θ cos 22 mat : θ π - 4 / : Rot Lorentz θ rot * : 41 line

Lorentz 0 Rot 2 1 sys

2D rotation [3D as well] follows the vector/matrix product rule, i.e: object*function

Define/generalise f v x Myfnct v x f * :

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v 12331 mat :

x f 1 x / 1 - :

Note that the 1D v*f(x) is scalar on the canvas. If you want to rotate the trace system, you must discretise each component and rotate each component individually.

plot f v 1 el x Myfnct f v 2 el x Myfnct f v 3 el x Myfnct 31 sys :

User multitrace, valued by 'v'

plot π 2 π 5 - 2 2 mat π - 2 π - 5 - 2 2 mat 3 1 sys

f v x Myfnct 12331 mat 1 x - (* x /

x π :

f v x Myfnct 1 π - π / 21 π - (* π / 31 π - (* π / 31 mat

f v x Myfnct 0.68169 - 1.36338 - 2.04507 - 31 mat

u π - :

f v u Myfnct 1 π + π / - 21 π + (* π / - 31 π + (* π / - 31 mat

f v u Myfnct 1.31831 - 2.63662 - 3.95493 - 31 mat

Purely numeric 1142522 mat / 1 - (1221 mat * 2 - 3 - 21 mat