Lorenz Attractor Script?

Next
 From:  bemfarmer
6403.1 
Discussion was started in the Duprin Cyclide topic.

For a Lorenz Script, the user enters a few start points, probably near each other.
If the origin is entered, an offset is assigned, say z = .001.
Each start point may be assigned a different color, to produce an arc of points, or MoI factory curve, of one color.
Each such trajectory is plotted as an arc of points, using the parametric equations derived
from "Euler's first-order linear approximation method," which approximate the differential equations. http://mathforum.org/library/drmath/view/61791.html

(Another way to do color would be to change the color based upon the iteration, but given only a few colors in a
typical MoI setup, rather than a progressive transition change in colors, this may not be the way to go?)

Now to select a script to use as a starting template...

- Brian
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
6403.2 In reply to 6403.1 
Well, like i mentioned in my previous post color would not be mandatory, imo… Or if the final spline shape could be broken in separate pieces (after sweeping) the user may colorize it in his/her 3D app afterwards.

Here's again the link, which shows nicely, in my opinion, how such attractors can look when swept and they don't have any color.

http://www.behance.net/gallery/MathRules-Strange-Attractors/7618879

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.3 
Yep that will be fun if you can transform this in real 3D surface or volume!

The best and easy program for strange attractor! But alas no possibility to save a 3D volume! ;(
Chaoscope!

http://www.chaoscope.org/

Try it! it's a true gem! Just with 3 keys! A task of ergonomy!





EDITED: 31 Dec 2013 by PILOU

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
6403.4 
A quick draft. Needs some work.
Attachments:

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
6403.5 
Oh, that was quick Brian! :-) Thank you very much. It's really nice that the user can set also the number of point!

Best regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
6403.6 In reply to 6403.5 
Hi Brian,

i like to ask if the script can be further enhanced so that it accepts equations too, to generate other Attractors?
I'm not sure if this is possible with MoI scripts , so just asking, if not i guess i can use your original script and
insert there other equations???

Best regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
6403.7 In reply to 6403.6 
I am an amateur programmer, with limited abilities.
A program like k3dsurf allows the entry of equations.
So a better programmer might be able to create a program to allow equation entry.

I have come across dozens of dozens of other attractors. Perhaps there are an infinite number?
For example, the Aizawa attractor has 6 parameters, a,b,c,d,e,f. Yet it still has 3 simple equations.
So these additional parameters could be added to the htm file.

http://jlswbs.blogspot.com/2011/10/aizawa.html

Alternatively, the code could be created to allow selection of pre-programmed attractors from a list. I was thinking of asking Michael how to do this in code, but one should first make an effort?
For example, to create a circle in MoI, first the circle command is selected, then another selection pops up to allow the choice of which type of circle
to create.

I started to add lineweb code to add a point output option, but ran out of energy that night :-)
Also thought about allowing the user to enter start points, or have 3 more inputs, x,y,z start points entry...

- Brian

EDITED: 6 Jan 2014 by BEMFARMER

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.8 
Seems Chaoscope above have all common attractors! ;)
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
6403.9 In reply to 6403.8 
@Brian - Thanks for the reply! I may check then the script and see what i can do.

@Pilou - Well, you can't save splines and process them in MoI, right…

Best regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.10 In reply to 6403.9 
<< Well, you can't save splines and process them in MoI, right…

Sure but you have all the formulas! ;)

http://www.chaoscope.org/manual.htm
---
Pilou
Is beautiful that please without concept!
My Gallery
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
6403.11 
Did an upgrade to the script, to version 2, with minimal testing.

Added optional ability to plot points, with code borrowed from Lineweb script.
Also entries for x,y and z, which cannot all be zero.

- Brian
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  BurrMan
6403.12 In reply to 6403.11 
Did you forget to attach version 2?
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.13 
Strange indeed! :)

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
6403.14 In reply to 6403.12 
Well, it was late.
Attachments:

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.15 
Excellent! Bravo!
A little trick : make the reseach of parameters inside Chaoscope then apply them inside moi!
http://www.chaoscope.org/
That will be more speady! ;)

Here I make the inverse because the Moi parameters were yet calculated! ;)



same parameters inside Chaoscope!
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
6403.16 
Elegant! :)

Sweep a circle then Twist and Array / Circular

EDITED: 10 Jan 2014 by PILOU

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Rich_Art
6403.17 In reply to 6403.16 
Cool effect. :-)

Peace,
Rich_Art. ;-)

| C4DLounge.eu | Our Dutch/Belgium C4D forum. |
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
 From:  Tommy (THOMASHELZLE)
6403.18 
I love all these scripts! :-)
Thank you so much!

I created another image for my website, this time based on a Lorenz Attractor ;-)
http://www.screendream.de

Cheers,

Tom
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged
 

Reply to All Reply to All