Chaos theory - Graphical represantation of a derivative calculation

Hi everyone,

I'm trying to represent on gh the Lorenz's attractor from the chaos theory as in this video :

I have the mathematical formula (see also in the video) :

dx/dt=a(y-x)

dy/dt=x(b-z)-y

dz/dt=xy-cz

I guess it's pretty simple but I just want to create the curve. Maybe it's just a question of variables. I tryed with different series and ranges but it was never the same as the "butterfly" shape I want.

Thanks.

Replies to This Discussion

Permalink Reply by David Rutten on January 14, 2016 at 10:19am

The equation is for derivatives, not position. Thus, each new point on the attractor is the result of the previous point as nudged by the equations. As such you cannot compute points independently, but you must compute them iteratively. You'll defeinitely need to resort to either Hoopsnake, Anemone, VB, C#, or python code.

Permalink Reply by peter fotiadis on January 14, 2016 at 12:27pm

What a paranoid idea (PS: I like chaos but that one is rather a handful)

Attachments:

Chaos_V4A.gh, 125 KB

Permalink Reply by peter fotiadis on January 15, 2016 at 1:27am

Added some "by the book" Lorenz chaos as Plan B.

For all that blame that man:

Attachments:

Chaos_V4B.gh, 123 KB

Permalink Reply by peter fotiadis on January 15, 2016 at 2:46am

And rather the best "by the book" option as Plan C.

Attachments:

Chaos_V4C.gh, 136 KB

Permalink Reply by Charlotte Le Dain on January 15, 2016 at 3:22am

Wouhaw! Thank you!

It's not as simple as I thought. I knew something was wrong but my mathematical classes are behind me...

And I don't know how to code. So thank you Peter for your time even if you feel a bit dizzy now. ;) It's totally understandable!

Permalink Reply by peter fotiadis on January 15, 2016 at 4:30am

Notify if you need to feel more dizzy than you ever imagined:

1001 curve examples [good news] are waiting for you - although strictly via code [bad news].

And a free bonus: the notorious Vodka ala Vodka (C)(TM)(US Patent pending) surface.

Moral: Docendo discimus.

Permalink Reply by Charlotte Le Dain on January 15, 2016 at 5:24am

It's seem pretty cool, I'm curious to see that even if I'll probably don't understand... It's fun though!

PS. What's a Vodka ala Vodka surface?

Permalink Reply by peter fotiadis on January 15, 2016 at 8:36am

Have a triple espresso [min] and give it a spin.

PS: The Vodka ala Vodka is what happens when you do penne ala Vodka and replace the pasta with Vodka (purely in the name of Science).

PS: Use the presets available in some defs (or if you are brave ... he he).

PS: Notify if you need more paranoid stuff.

best

Attachments:

Curves_V1.gh, 237 KB

Permalink Reply by Charlotte Le Dain on January 15, 2016 at 10:21am

Thanks, I'll try to learn a bit. ;)

In the meantime, this butterfly is soooo gorgeous! Magnifique!

I'm not sure what to think about the Vodka ala vodka but really nice and weird job. The fusilli in marvelous!

And without knowing you gave me a great way to modelize a spiral which is what I'm working on. Milles merci!

PS. I'm trying to do a bunch of paranoid stuff for my architecture diploma. :)

best

Permalink Reply by peter fotiadis on January 15, 2016 at 10:34am

Spiral? then get this and enjoy (spot the auto-zoom capability in some defs). Free bonus: the Vodka curve (what else?, he he)

PS: Paranoid stuff aplenty around me > mild > wild > freaky > you name it (but the bad news are ... well ... you know them already).

PS: Jokes apart ... well ... I do hope that you know what actually means when you do a paranoid skin for some building (LOT'S of details are required: NEVER allow your mind to walk that walk UNLESS you fully understand the price [metaphorically AND literally] to pay, he he). Been a student or a pro makes absolutely no difference, mind.

Moral: triple red pepper Vodka anyone?

Attachments:

spiral_and_Goldspiral6.gh, 147 KB

Permalink Reply by Charlotte Le Dain on January 15, 2016 at 11:11am

What a curve!

Don't worry, I'm doing research for now. The best way to do crazy stuffs and experiments! Of course I know what's involve those skins.

PS. Kind of curious to taste your "Heaven can wait" cocktail...

Thanks again and again!

Permalink Reply by peter fotiadis on January 15, 2016 at 11:43am

BTW: It's not strictly a cocktail, mind (but is nuclear).

BTW: Whilst doing the research don't forget this:

that in the eye of the ignorant has nothing to do with Lorenz freaky skins (not to mention the Fusilli ala Fusilli (C)(TM)(US Patent pending) surface - nothing to do with the Fusilli ala Vodka, mind) ... but in fact ... well ... it's the most important part of the equation, he he