Bracelet design generated through Rhino Scripting. First of all, the Pickover Strange Attractor is scripted. For more information on Pickover Attractors, you can check http://www.chaoscope.org/ .

Then, each point in the Pickover Attractor point cloud is evaluated. The nearest 7 points to each point is found and connected to the input point.

Thanks a lot to Seda Zirek for her help in the point connection code.

(http://mel-examples.blogspot.com/)

Pickover Strange Attractor code

Option Explicit

‘Script written by Elif Erdine

Call Pickover()

Sub Pickover()

Dim i

Dim x()

Dim y()

Dim z()

Dim pt()

Dim maxpoints

maxpoints = 20000

Dim A, B, C, D

A= -0.759494

B= 2.449367

C= 1.253165

D= 1.5

ReDim Preserve x(maxpoints)

ReDim Preserve y(maxpoints)

ReDim Preserve z(maxpoints)

x(i) = 0

y(i) = 0

z(i) = 0

i=0

Do While (i < maxpoints)

x(i+1) = Sin(A * y(i)) – z(i) * Cos(B * x(i))

y(i+1) = z(i) * Sin(C * x(i)) – Cos(D * y(i))

z(i+1) = Sin(x(i))

ReDim Preserve pt(i)

pt(i) = Array(x(i), y(i), z(i))

If IsArray(pt(i)) Then

Call Rhino.AddPoint(pt(i))

‘ Dim plane

‘ plane = Rhino.PlaneFromNormal(pt(i), Array(0,0,1))

‘ Call Rhino.AddCircle(plane, 0.2)

End If

i = i+1

Loop

End Sub

Point Connection code

Call ConnectPoints()

Sub ConnectPoints()

Dim ptcloud, ptall

ptcloud = Rhino.GetObject(”input pointcloud”, 2, True, True)

If IsNull(ptcloud) Then Exit Sub

ptall = Rhino.PointCloudPoints(ptcloud)

If IsNull(ptall) Then Exit Sub

Dim i

Dim ptnearest

For i=0 To UBound(ptall)

Dim arrPtall : arrPtall = functNearestNeighbor(ptall, i)

Dim strLine1 : strLine1 = Rhino.AddLine(ptall(i), arrPtall(0))

Dim strLine2 : strLine2 = Rhino.AddLine(ptall(i), arrPtall(1))

Dim strLine3 : strLine3 = Rhino.AddLine(ptall(i), arrPtall(2))

Dim strLine4 : strLine4 = Rhino.AddLine(ptall(i), arrPtall(3))

Dim strLine5 : strLine5 = Rhino.AddLine(ptall(i), arrPtall(4))

Dim strLine6 : strLine6 = Rhino.AddLine(ptall(i), arrPtall(5))

Dim strLine7 : strLine7 = Rhino.AddLine(ptall(i), arrPtall(6))

i=i+1

Next

End Sub

Posted: June 11th, 2009 under Parametric Design.
Comments: 1

Gumowski-Mira attractors were developed at the CERN research centre in 1980 by I. Gumowski and C. Mira while aiming to calculate the trajectories of sub-atomic particles. They create organic patterns resembling natural/marine forms.

Option Explicit

‘Script written by Elif Erdine

Call GumowskiMira()

Sub GumowskiMira()

Dim i

Dim x()

Dim y()

Dim pt()

Dim maxpoints

maxpoints = 5000

Dim B

B = 1

ReDim Preserve x(maxpoints)

ReDim Preserve y(maxpoints)

x(i) = 0

y(i) = 5

i=0

Do While (i < maxpoints)

x(i+1) = B*y(i) + GM(x(i))

y(i+1) = GM(x(i+1)) – x(i)

ReDim Preserve pt(i)

pt(i) = Array(x(i), y(i), 0)

If IsArray(pt(i)) Then

Call Rhino.AddPoint(pt(i))

Dim plane

plane = Rhino.PlaneFromNormal(pt(i), Array(0,0,1))

Call Rhino.AddCircle(plane, 0.2)

End If

i = i+1

Loop

If IsArray(pt) Then

Dim ptcloud

ptcloud = Rhino.AddPointCloud(pt)

End If

Dim ptdel

ptdel = Rhino.GetObjects(”select points to delete”, 1, , , True)

Call Rhino.DeleteObjects(ptdel)

End Sub

Function GM (ByVal x)

Dim A

A= 0.305

GM = A*x + 2*(1-A)*x^2 / (1+x^2)

End Function

Posted: April 16th, 2009 under Parametric Design.
Comments: 1

Rossler attractor behaves similarly to Lorenz attractor. It’s formed by 3 non-linear ordinary differential equations. ( http://en.wikipedia.org/wiki/Rossler_map )

 

 

Call Rossler()

Sub Rossler()

            Dim x, y, z

            Dim maxpoints

            maxpoints = 8000

            Dim h

            h = 0.025

            Dim p(2)

            Dim ptnew()

            Dim i

            Do While (i<maxpoints)

                        p(0) = p(0) + h* dx(p(0), p(1), p(2))

                        p(1) = p(1) + h* dy(p(0), p(1), p(2))

                        p(2) = p(2) + h* dz(p(0), p(1), p(2)) 

                        Rhino.AddPoint(p)

                        ReDim Preserve ptnew(i)

                        ptnew(i) = p

                        i=i+1                

            Loop

           

            Call Rhino.AddCurve(ptnew, 3)

End Sub

 

 

Function dx(ByVal x, ByVal y, ByVal z)

            dx = -y-z

End Function

Function dy(ByVal x, ByVal y, ByVal z)

            dy = x + 0.4*y

End Function

Function dz(ByVal x, ByVal y, ByVal z)

            dz = 0.31 + z*(x-5.3)

End Function

 

Posted: April 16th, 2009 under Parametric Design.
Comments: none

I’ve recently started using Rhino Scripting as a design tool in my research. I will be documenting here my learning process through the .rvb scripts.

This study shows the Curlicue Fractal, which generates quite intricate patterns. (http://mathworld.wolfram.com/CurlicueFractal.html)

 

Call Curlicue()

Sub Curlicue()

            Dim f

            Dim i

            Dim j

            Dim pi

            pi = Rhino.Pi

            Dim sqtwo

            sqtwo = 1.4142135623730950488016887

            Dim eulers

            eulers = 0.577215664901532860606512

            Dim golden

            golden = 1.618033988749894848204586

            Dim lntwo

            lntwo = 0.69314718055994530941

            Dim e

            e= 2.71828182845904523536028747

            Dim p(2)

            Dim ptCur()

            

            For j=0 To 50000*pi Step sqtwo*pi*2

                       

                        f = f + j

                        p(0)= p(0) + Cos(f)

                        p(1)= p(1)+ Sin(f)

                        p(2)=p(2) + Cos(f)*Sin(f)

                       

                        ‘Rhino.AddPoint(p)

                        ReDim Preserve ptCur(i)

                        ptCur(i) = p

                        i=i+1

                       

            Next

            Call Rhino.addcurve(ptCur, 3)       

 

End Sub

Posted: April 16th, 2009 under Parametric Design.
Comments: none

A wine bottle generated in GC. The form itself is created by a series of quartic curves, whose radii are parametrically interrelated to each other.

( http://mathworld.wolfram.com/QuarticCurve.html )

The ornamental pattern is created by firstly forming tubes that pass through the diagonals of one component and then creating hyperbolic curves whose midpoints meet in the centroid of the component. The hyperbolic curves are then lofted with each respective edge of the component, forming planar surfaces.

 

 

 

Posted: February 28th, 2009 under Parametric Design.
Comments: none

A canopy design created in Generative Components by the population of 3d parametric components.

A series of canopies that are created by just updating the definitive geometry will be uploaded soon..

Posted: April 7th, 2008 under Parametric Design.
Comments: none

 

A recent rib structure study developed in GC.

The depth of the ribs is controlled by a variable which is calculated in relation Dot.Product function. Dot Product: In mathematics, the dot product, also known as the scalar product, is an operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. It is the standard inner product of the Euclidean space.In Euclidean geometry, the dot product, length, and angle are related: For a vector a, a•a is the square of its length, and, more generally, if b is another vector, a * b = |a| *|b| *cos(?) where|a| and |b| denote the length (magnitude) of a and b , and ? is the angle between them. Since |a|cos(?) is the scalar projection of a onto b, the dot product can be understood geometrically as the product of the length of this projection and the length of b.

(http://en.wikipedia.org/wiki/Dot_product )

The variable created in this example takes the Arccosine of the Dot Product for 2 vectors, which are the Z direction of the base coordinate system and the Z direction of the coordinate system created on the surface. Since the result will be an angle between 0 and 180, the Arccosine of the Dot Product is divided to 180, thus producing a variable between 0 and 1.

 

Posted: March 15th, 2008 under Parametric Design.
Comments: none

 

I’ve attended the Smart Geometry 2008 Workshop and Conference, which was held on February 27th- March 5th, in Munich.

The workshop structure was comprised of 5 different categories, namely Environment, Fabrication, Form, Computation, and Architecture.  I was part of the Computation group, looking into ways of scripting and manipulating mathematically defined forms in GC.  My goal was to develop YME’s proposal for the AADRL.TEN Pavilion, basically defining the underlying geometry, the mobius-klein nonmanifold, in a parametric manner inside GC and then populating this geometry with components of varying depths and openings. In GC script, it is possible to describe any geometry with an explicit formula. Thus, by defining the x, y, z parameters of the surface and inserting variables for its sub-domains in GC script, it was possible to visualize any part of the surface by changing the sub-domain variables. Afterwards, four types of simple components with different depths and openings were assigned to the UV coordinates to populate the 4 sub-domains of the mobius-klein nonmanifold.  

 

Mobius-Klein nonmanifold scripted in GC.

Sub-domain of the surface visualized by changing variables.

Sub-domain populated with one type of component.

 

 

 

 

Posted: March 11th, 2008 under News, Parametric Design.
Comments: none

Elif Erdine and Ceyhun Baskin have been the guest editors of Betonart for its Winter 2008 issue, investigating the impact of concrete and digital technologies upon one another under the theme “Digital Concrete”. Their article “Towards a Paperless Architecture” have been published alongside with articles from Christos Passas (ZHA), Charles Walker (ZHA), Andrew Murray (AKT), and Wolfgang Rieder (Rieder FiberC).

Read more »

Posted: March 11th, 2008 under Architecture, News, Parametric Design.
Comments: none

The AADRL.TEN Competition was organized in October by the AA Design Research Lab (DRL) to rethink and celebrate its 10th anniversary. More than 30 proposals were submitted by postDRL designers. YME has been selected as one of the 5 finalists with their parametrically generated pavilion.

 

 

This proposal aims to capture 10 years of DRL explorations of new forms of design thinking in a realized tangible structure. The pavilion presents itself as a non-orientable manifold where there is no clear distinction between inside and outside. It offers a unique and intriguing spatial experience that will serve as a teaching instrument for the academic community. The design pushes the structural properties of fiber-C by proposing an innovative use of this material as a modular, self-supporting assembly.

 

The shape of the pavilion is mathematically generated by combining the properties of two non-orientable manifolds, the klein bottle and mobius strip. The pavilion measures 10×7x4 meters and is intended to be a freestanding structure without anchoring to the ground.

 

The curved surface of the manifold is constructed out of plannar fi ber-C panels that are folded into parallelepipeds forming ‘cells’ that are connected together to form the curvature. Paracloud software is used to populate the geometry with components. More information about the competition can be found at 

http://www.aaschool.ac.uk/aadrl/drlpavilion/ 

     

Posted: December 4th, 2007 under News.
Comments: none