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I had some hesitation, I don't know really where post this message (since the
picture was calculated under Povray).
It is about a brownian motion without random numbers, during some graphics
programming tries I have found a method to obtain a brownian motion without
random numbers. I explain with a little algorithm:
x = 1.0
y = 1.0
z = 1.0
d = 3.6
i = 0
iter = 5000 // number of particles //
while (i<iter)
xnew = x + cos(z*dt)
ynew = y + sin(z*dt)
znew = z - (x*y*dt)
plot(<xnew,ynew>)
x = xnew
y = ynew
z = znew
endwhile
I am not a mathematician, I just use some mathematicals tools for my hobby.
Lionel.
--
Do not judge my words, judge my actions.
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Attachments:
Download 'brownian_motion.jpg' (75 KB)
Preview of image 'brownian_motion.jpg'
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It /looks/ brownian indeed.
Interesting.
Thomas
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Fractracer wrote:
> It is about a brownian motion without random numbers, during some graphics
> programming tries I have found a method to obtain a brownian motion without
> random numbers.
Another way to look at this would be to say you found a
formula for generating reasonable random numbers ;)
Post a reply to this message
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> Fractracer wrote:
>
>> It is about a brownian motion without random numbers, during some
>> graphics
>> programming tries I have found a method to obtain a brownian motion
>> without
>> random numbers.
>
> Another way to look at this would be to say you found a
> formula for generating reasonable random numbers ;)
Indeed, it seems like a formula for random numbers, but I have not
enough mathematical knowledge to see if it is really efficient.
--
Do not judge my words, judge my actions.
---
http://www.avast.com
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Le 14/02/2014 14:38, FractRacer a écrit :
> Le 13/02/2014 23:28, Christian Froeschlin a écrit :
>> Fractracer wrote:
>>
>>> It is about a brownian motion without random numbers, during some
>>> graphics
>>> programming tries I have found a method to obtain a brownian motion
>>> without
>>> random numbers.
>>
>> Another way to look at this would be to say you found a
>> formula for generating reasonable random numbers ;)
>
> Indeed, it seems like a formula for random numbers, but I have not
> enough mathematical knowledge to see if it is really efficient.
>
The "formula" is not random. It looks erratic, but is not. If you know 1
set of coordinates, you can predict the next ones.
If you are interested on random number without a real source of
randomness, you will get most interesting search results with:
PRNG pseudo random number generator
They usually requires the usage of a hidden state, the generated random
value being only a part of that full state. (such as using a 32 bits
number as internal state, and returning only 16 bits number as random value)
Of course, you know that povray has its own prng... available with
seed() and rand().
--
Just because nobody complains does not mean all parachutes are perfect.
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Le 17/02/2014 08:01, Le_Forgeron a écrit :
> The "formula" is not random. It looks erratic, but is not. If you know 1
> set of coordinates, you can predict the next ones.
>
> If you are interested on random number without a real source of
> randomness, you will get most interesting search results with:
> PRNG pseudo random number generator
>
> They usually requires the usage of a hidden state, the generated random
> value being only a part of that full state. (such as using a 32 bits
> number as internal state, and returning only 16 bits number as random value)
>
> Of course, you know that povray has its own prng... available with
> seed() and rand().
>
Yes the formula is not random, but how differentiate a real random
sequence and a pseudo-random sequence like mine? I actually try to study
this mathematicals phenomenons.
In fact, while I was looking for formulas like Lorenz Butterfly, I was
surprised by the drawing of the formula I wrote. As I have already said
I have not enough mathematical knowledges, but I know a little what is a
brownian motion, and the act of obtaining this /randomness/ curves with
non random calculations intrigue me.
Lionel.
--
Do not judge my words, judge my actions.
---
Ce courrier électronique ne contient aucun virus ou logiciel malveillant parce que la
protection avast! Antivirus est active.
http://www.avast.com
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