0d6ef658-c627-400f-b8d5-f95ff90a901b 40 6 9 decimal

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

Brownian motion: imitate

t0 1 time :

Keep trying many runs, you will get various beautiful images. The size of the image depends upon the random generation. The running time depends upon the size of the x/y Brownian.

Unform ... -1 < rnd < 1 n rnd μ n : 2 μ Random * 1 - 21 line :

1 rnd 1 el Un-nest ≡

N 5000 :

Generate recursive x/y
Cartesian Brownian motion Ω x 1 el 0 : y 1 el 0 : 12 mat i 2 N range x i el x i 1 - el 1 rnd 1 el + : y i el y i 1 - el 1 rnd 1 el + : 21 line for i 1 N range X i el x i el 0 round abs : Y i el y i el 0 round abs : scan for matched pairs-> fill white X i el Y i el * 0 ≠ Ω X i el Y i el el 255 : Not Brownian if 51 line for Ω 41 line :

Notes: 0. Work sheet AutoCal OFF 1. Update 'N' ... F9 2. Reset original size 2. Optimiz Numeric

jmGiraud: 20160822

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 Ω

1 time t0 - 171 sec *

N 1000 :

Brw x 1 el 0 : y 1 el 0 : 12 mat i 2 N range x i el x i 1 - el 1 rnd 1 el + : y i el y i 1 - el 1 rnd 1 el + : 21 line for x y augment 31 line :

Highlight a sub region

start 1 :

<= start of sub

end 100 :

<= end of sub

sub Brw start end 12 submatrix :

Brw sub 2 1 sys

About the highlight sub region: In this typical "start = 1", some Brownian experiments will highlight an entire region, uniquely. We can say so, knowing that Smath quick plot 2nd trace does not override the 1rst one.

Brownian motion

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 x x t el x Max eval / : t y y t el y Max eval / : 61 line

τ 2 N range :

Brownian motion [Collaboration: jmG/BER7]

t 2 ≡ path t x t y 1 2 mat : path path t x t y 1 2 mat stack : if t x t y . 12 red 1 5 mat 2 1 sys