29c5f410-363f-4bda-8e2f-2ace8941596a 15 3 5 decimal

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

1. Animate Lissajous [circulation]

Lissajous preparation t fX 1.5 t sin * : t fY 0.75 2 t * sin * : start 0 : end 2 π * : 12 mat t start end start 0.05 + (range : 51 line

i 1 t rows range X i el t i el fX eval : for

i 1 t rows range Y i el t i el fY eval : for

Lissajous X Y augment : t x X t el : t y Y t el : 12 mat N Lissajous rows : FRAME 1 N 2 range : 41 line

Lissajous t x t y . 12 black 1 5 mat 3 1 sys

The variable of animation is "user". Make it visible. Once the work sheet has finished accumalating X, Y and the plot is setup, select FRAME in the drop down graph menu.

N 126

2. Animate Brownian motion [unpredictable accumulation]

u Max u min abs u max ≥ u min abs u max if :

Generate recursive x/y
Cartesian Brownian motion N 500 : x 1 el 0 : y 1 el 0 : i 2 N range x i el x i 1 - el 21 Random * 1 - (1 el + : y i el y i 1 - el 21 Random * 1 - (1 el + : 21 line for t U x t el x Max eval / : t V y t el y Max eval / : 61 line

ANIM 2 N range :

Brownian motion [Collaboration: jmG/BER7]

t 2 ≡ path t U t V 1 2 mat : path path t U t V 1 2 mat stack : if t U t V . 12 red 1 5 mat 2 1 sys

Observe: in the Brownian, neither 'x' or 't' is a canvas variable. It does not appear in the drop down "Animate" menu.

3. Butterfly project [predictable accumulation]

t Φ 24 t * cos * 110 / t * sin (5^+ : t fX t sin t cos exp t Φ - (* : t fY t cos t cos exp t Φ - (* : start 1 π * - : end 1 π * : 12 mat t start end start 0.025 + (range : 51 line

cumulative animations in the Smath document

i 1 t rows range X i el t i el fX eval : for

i 1 t rows range Y i el t i el fY eval : for

Butterfly X Y augment :

N Butterfly rows : 252

CUMUL 1 N 2 range :

------------------------>

t fx X t el : t fy Y t el : 12 mat

Butterfly [Collaboration: jmG/BER7]

t 1 ≡ path t fx t fy 1 2 mat : path path t fx t fy 1 2 mat stack : if t fx t fy . 12 red 1 5 mat 2 1 sys

t start end start 0.005 + (range :

i 1 t rows range X i el t i el fX eval : for

i 1 t rows range Y i el t i el fY eval : for

butterfly X Y augment : sub1 butterfly 162412 submatrix : sub2 butterfly 625125712 submatrix : 31 line

sub1 sub2 2 1 sys