Looking more into Python, the syntax and how you can use for loops, Rhinocommon and math within the GH Python Component, I decided to write and share this animated Python script of a Rossler attractor. This particular attractor lies in the context of particle kinematics within chemical reactions. This system is defined by three non-linear ordinary differential equations originally studied by Otto Rössler. I find it to be, an extremely interesting and minimally beautiful system, mainly due to the particle’s easily observed movement in the Cartesian 3D space.

Thy python code looks something like this:

## #”Rossler Attractor Grasshopper Python Component”

#Written by Marios Tsiliakos on 22/11/2012

#Based on the equations provided by Paul Bourke http://paulbourke.net

#Rossler Attractor by Marios Tsiliakos is licensed under a

#Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

#Based on work at http://www.digitalsubstance.wordpress.com.## #Imports

from math import *

import _random as rnd

import Rhino## # Subfunction

def Rossler(it):

#random number

r=rnd.Random(Seed)

r0 = r.random()*0.1

# set the constants

a = 0.15 + r0

b = 0.2 – r0

c = 5.7 + r0

h = H

var.append((round(a,2),round(b,2),round(c,2)))

# provide the initial point

x,y,z=0.1,0.0,0.0

for i in range(it):

x0= x + h*(-y -z)

y0= y + h*(x + a*y)

z0= z + h*(b+z*(x-c))

#make the resulting coordinates the coordinates last point

x,y,z = x0, y0, z0

pts= Rhino.Geometry.Point3d(x,y,z)

arrPts.append(pts)## #Main function

if Iterations == None:

Iterations = 1000

if H == None:

H = 0.05

if Seed == None:

Seed = 2## if Run== True:

#global lists

arrPts = []

var =[]

# always provide the creation of a curve by sufficient number of points

numpoints =counter+4

if numpoints < Iterations:

Rossler(numpoints)

crv = Rhino.Geometry.Curve.CreateInterpolatedCurve(arrPts,3)

counter+=10

print counter

print “Rossler attractor with values: a =” , var[0][0],”b=” , var[0][1],”c=”, var[0][2],”h=” , H

if numpoints >= Iterations:

print “goal achieved”

# Comment out the next line to get the resulting points

#Rossler(Iterations)

#crv = Rhino.Geometry.Curve.CreateInterpolatedCurve(arrPts,3)

#counter = Iterations

#outputs

Ross=crv

Points = arrPts

else :

print(“Idle”)

counter = 0

And here is a snapshot of the definition . You can download it at the usual place.

Enjoy!