Attraktors [Generative equation]



Hi everyone

I present a script that I developed on “blender” to generate attraktors.
All Attraktors:
http://www.gael-labousse.com/images/temp/Attraktor/Final_Aizawa.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_DequanLi.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_Hadley.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_Halvorsen.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_QiChen.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_SprottLinzL.jpg
http://www.gael-labousse.com/images/temp/Attraktor/Final_Thomas.jpg

Here is my reference [Chaotic Atmospheres]. (made with cinema 4D plugin)
http://chaoticatmospheres.com/125671/workflows

and this site where I found the mathematical equations. [Jürgen Meier]
http://www.3d-meier.de/index.html

5 Likes

So beautiful, loving the shapes especially with that wooden material on white bg :slight_smile: Everything is just perfect!

An excellent way to present code :smiley:

Thank you! :slight_smile:
I like to combine art and programming, aesthetic and technical in my compositions

Nicely done indeed. The shapes are very harmonious.

great !

there a few months ago:


very nice, I assume you got the idea from him. https://www.behance.net/gallery/7618879/MathRules-Strange-Attractors

imagecorp:
Nice! This is done with a script?

alan.zirpoli:
Yes of course, it’s ma référence. I love the work of this Digital Artist. I tried to pay tribute to him with blender :slight_smile:

really beautiful. Maybe it would be great to have this as an add-on. I have no idea of how to do it, but i was just thinking on it :wink:
Again: great idea and great art.

Hello Gamel, that looks very beautiful. I have tried your script. But the script has problems under Blender 2.72b. It looks that are problems with the convertion from cube to nurbs. But i haven`t enough knowledge about python to change the script. Can anyone try to change the script so it runs under 7.72b. Thanks.

looking nice
but where is the link for the script ?

happy bl

There is no link, the script is on the pictures. You have to write it in the blender text editor and press the button “run script”.

Hi

Mikel007:
" Can anyone try to change the script so it runs under 7.72b. Thanks."

…7.72??? hahaha ^^ I create this project with blender 2.72b, and I have not had a problem: /

I will spend my scene to test :wink: >>> LabousseGael_AttraktorsScript.blend (513 KB)


beautiful fluid forms

Great work!! love it

These are amazing! The results are almost like furniture that can be 3d printed.

Many thanks for that. It runs on my PC, too. And Blender 7.72b - it will come, guarantee :slight_smile: I hope i find the problem that i have with the other script (it was the Thomas-Attraktor).

Ey, I’m really glad you share this, I’m having lots of fun with them.
I was trying to make a very sutil adjustment in the initial parameters and then apply it as a shape key, but I can’t get a fluid transition.
Am I missing something? or is just the nature of this attractors?

import bpy
import math

# Equations ///////////////////////////////// The Aizawa Attractor
# dx/dt = (z-β)*x-δ*y
# dy/dt = δ*x+(z-β)*y
# dz/dt = ɣ+α*z-(z**3/3)-(x**2+y**2)*(1+ε*z)+ζ*z*x**3

x0 = 0.1
y0 = 0
z0 = 0
i = 0
j = 0
w = 0

# Parametres
ε = 0.3
α = 0.95
ɣ = 0.6
δ = 3.5
β = 0.7
ζ = 0.1
Facteur = 10
Delta = 0.01

# Compteurs
t = 15000
Step = 25

# Listes
PointX = []
PointY = []
PointZ = []
VertexX = []
VertexY = []
VertexZ = []

def CalcPoints():
    
    x=x0
    y=y0
    z=z0
    for i in range (1,t):
        dx = (z-β)*x-δ*y
        dy = δ*x+(z-β)*y
        dz = ɣ+α*z-(z**3/3)-(x**2+y**2)*(1+ε*z)+ζ*z*x**3
        x=  x + Delta * dx
        y=  y + Delta * dy
        z=  z + Delta * dz
        PointX.append(x)
        PointY.append(y)
        PointZ.append(z)
    
    subslistlen = int(len(PointX) / Step)
    for i in range (subslistlen):
        VertexX.append (PointX[ i * Step ])
        VertexY.append (PointY[ i * Step ])
        VertexZ.append (PointZ[ i * Step ])
    
def Aizawa():
    
    CalcPoints()

    bpy.ops.mesh.primitive_cube_add()
    bpy.data.objects["Cube"].name = "Aizawa"
    bpy.ops.object.editmode_toggle()
    bpy.ops.transform.resize(value=(0, 0, 0))
    bpy.ops.mesh.remove_doubles()
    obj  = bpy.data.objects['Aizawa']
    mesh = obj.data
    
    for j in range (len(VertexX)):
        bpy.ops.mesh.extrude_region_move(TRANSFORM_OT_translate={"value":(0,0,0)})
    
    bpy.ops.object.editmode_toggle()
    
    for j in range (len(VertexX)):    
        vert = mesh.vertices[j] 
        vert.co[0] = VertexX[j]*Facteur
        vert.co[1] = VertexY[j]*Facteur
        vert.co[2] = VertexZ[j]*Facteur
        
    bpy.ops.object.convert(target='CURVE')
    bpy.ops.object.editmode_toggle()
    bpy.ops.curve.spline_type_set(type='NURBS')
    bpy.data.curves['Aizawa'].resolution_u = 3       
    bpy.ops.object.editmode_toggle()

def shKey():
    
    bpy.ops.object.shape_key_add(from_mix=False)
    bpy.ops.object.shape_key_add(from_mix=False)
    
    CalcPoints()
    
    for w in range (len(VertexX)) :
        shKDATA=bpy.data.objects['Aizawa'].data.shape_keys.key_blocks['Key 1'].data[w]
        shKDATA.co[0] = VertexX[w]*Facteur
        shKDATA.co[1] = VertexY[w]*Facteur
        shKDATA.co[2] = VertexZ[w]*Facteur

Aizawa()

x0 = 0.101
y0 = 0.001
z0 = 0.001
ε = 0.3
α = 0.95
ɣ = 0.6
δ = 3.5
β = 0.7
ζ = 0.1
Facteur = 10
Delta = 0.01

del PointX[:]
del PointY[:]
del PointZ[:] 
del VertexX[:] 
del VertexY[:]
del VertexZ[:]

shKey()

It was a cool coincidence the day you posted this on blendernation I finished doing some test renders. I continued my work today this is what I came up with using a blender addon called strange attractors… By the way I really like your renders! :smiley: Cheers Markus


elZancudo:
I do not know, I’m not very good at programming. I am always surprised to have managed this script ^^ But I’ll see that during the holidays

LarelZe:
I did not know there was an addon to do. I knew that a “plugin” existed in C ++ on Cinema 4D but that’s all.

Thank you all! I think making a movie for the holidays if I have time ^^