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

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

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!

A quick draft. Needs some work.

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

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

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

Seems Chaoscope above have all common attractors! ;)

@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

<< 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

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

Did you forget to attach version 2?

Strange indeed! :)

Well, it was late.

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!

Elegant! :)

Sweep a circle then Twist and Array / Circular

Cool effect. :-)

Peace,
Rich_Art. ;-)

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