9ee0c31b-be75-479b-862c-dc398b968724 24 6 9 decimal

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

Lorenz attractor .. finite differences.

t0 1 time :

Algo style f(2), g(2): 3 non-linear running in the two directions. 
Observe the non-indexed "for loop" that will autofill/accumulate
while running  dynSys [,,,,,] over "NumIt" 2 f 2 g xo NumIt dt dynSys initialise 't & x' with xo t xo : x xo : 12 mat k 1 NumIt range t t dt t t r g f * + eval : x x t augment : 21 line for x 41 line :

0.1 0.2 0.3 13 mat

281083 / 13 mat

In there: 'u' & 'r' are two dummies x r Ctrl 0 : x u Lorenz 5 x 2 el x 1 el - (* x 1 el x 3 el * - 15 x 1 el * + x 2 el - x 1 el x 2 el * 1 x 3 el * - 31 mat : 21 line

xo 0.1 0.2 0.3 13 mat transpose :

NumIt 500 :

(any1,any2) are simply the start/maintain "dynSys" global algo => upto NumIt Sol any1 any2 Lorenz any1 any2 Ctrl xo NumIt 0.02 dynSys :

Collect the triplet in compactum x1 Sol 1 row transpose : x2 Sol 2 row transpose : x3 Sol 3 row transpose : 13 mat

1 time t0 - 49 sec *

x3 x2 augment x3 x1 augment x2 x1 augment 3 1 sys Sol transpose

Setup the non-linear triplet idx i 1 NumIt 1 + range idx i el 0.1 i * : for idx 21 line :

idx x1 augment idx x2 augment idx x3 augment 3 1 sys

L x3 x1 augment : θ rot θ cos θ sin - θ sin θ cos 22 mat : θ π - 2 / : Rot L θ rot * : 41 line

CWD C:\SmathFile CurrentDirectory :

Rot CWD Lorenz wfile 1

Rot CWD Lorenz rfile :

0 Rot 2 1 sys

N NumIt :

τ 1 N range :

x Rot 1 col : y Rot 2 col : 12 mat

t x x t el : t y y t el : 12 mat

0 Rot t x t y . 12 black 1 5 mat 3 1 sys

Create/accumulate 0 t 1 ≡ path t x t y 12 mat : path path t x t y 12 mat stack : if t x t y . 12 black 15 mat 21 sys 21 sys