We started with a group of particles flocking. From that, we traced the areas where the particles have traveled to understand their movement better. We would like for these paths to become a skin to a building. Next we would like to have the particles to move along a surface that in the end would be a structure.

The ants are moving around and are leaving a "trail" now that is marking their path. next, you might start to take these trails and apply the pattern towards a facade to pattern a potential material change on that facade

the output of a script i wrote in processing that documents the rules of the ca instead of just on/off.

cellular automaton acceleration rules

my project creates a new set of rules for the cellular automaton-- acceleration rules-- determined by the change of rules from one line to the next. instead of outputting on/off or black/white, these new rules imply a 3dimensional move (as documented in green).

when these moves are joined and swept, a 3dimensional fabric of the ca is created.

GA Wall Diagram

GA Wall Lighting

Here we move from an opaque wall of cube units to one that tansmits light when all the units finally become spheres. The units transform uniformly in this instance.

GA Wall Intro

The premise of my project is to use a cellular unit like the cube and transform it's continuity setting over a period of time so that it becomes a sphere. A random continuity value can then be applied to many units to create a varied effect.

Ant Movement

This is the animation and the script that is moving our "ants" around and stopping them at the food source. The next step of the process is to have them start to return to back to the "colony"

Bloom and Neil

//ant script
//create food nodes//assign for loop to assign number of nodesfor($n=1;$n<6;$n++){//assign nodename="node" c="rand(-30,30);$d="rand(-30,30);move" j="1;$j<5;$j++){" name="ant" i="1;$i<300;$i++){" 10="="0)" a="{rand(-1,1),rand(-1,1),rand(-1,1),rand(-1,1)};" b="{rand(-1,1),rand(-1,1),rand(-1,1),rand(-1,1)};}" k="1;$k<5;$k++){" ant="ant" overlap="false;" h="1;$h<6;$h++){" ax =" eval(" az =" eval(" node="node" nx =" eval(" nz =" eval(" diffx =" abs((float)($ax-$nx));" diffz =" abs((float)($az-$nz));" overlap="true;" overlap="=">

wind effect for possible crystal growth

l-system images

I posted another view of the an animation that is in plan view so that it is easier to see how the spheres are moving

competing radial fields

Newton Field with radial influence

This is adding radial fields to influence the orbit of the spheres as they move about the "food source" (newton field).

This is using a Newton field to show a very rought way of ants being affected by a food source.

Flocking

Controlling each object and how they move

Controlling the groups, but not the individual particals.

Animation

This is a partial animation of spine vertebrae blending into subsequent ones. My intention is to ghost the whole spine in the background so that it is clear what the animation is showing.

For Loop

I was trying to abstractly mimic the shape of the vertebrae of the spine, which is the concentration of my divergent evolution model. I had trouble switching it to be smaller at the top so that it would look like the real shape of a spine.

loop

percolation sections

dynamic gear update

update:

here is a video update of the gear rotated with dynamic animation using particles

Fountain

Here is a screen shot of an animation of a fountain I made using particles

dynamic gear rotated by particles

i have been trying to use particles as a dynamic force within maya to simulate brownian motion.

i was able to create particles with a turbulent force acting upon them which i could use to simulate the air or liquid particles which cause brownian motion, but have been unable to find out how to make the particles move a rigid body, in attempt to be able to do this i completed this tutorial which rotates a gear using particles under a gravitation force field.  i created a script for this gear and placed it along with the maya file in the courses drive in the directory:

Spring 08 Courses/COURSES/326C_pattern formation/Brownian Motion

Loop, Rotate, Weave

The script generates a polysurface and then copies, offsets and rotates it until the final polysurface in the sequence is generated. Then the weave script creates a weave for the topmost polysurface.

snowflake

Bibliography

The following books are on reserve in the library:

Kostas Terzidis Algorithmic Architecture Oxford ; Burlington, MA : Architectural Press, 2006. NA2728 .T44 2006

Kostas Terzidis Expressive Form: a Conceptual Approach to Computational Design London; New York : Spon Press, 2003. NA2500 .T46 2003

Anthony Burke and Therese Tierney, (eds) Network Practices: New Strategies in Architecture and Design New York : Princeton Architectural Press, c2007 NA2543.T43 N48 2007

Therese Tierney Abstract Space: Beneath the Media Surface London; New York: Taylor & Francis, 2007. NA2584 .T54 2007

Dollens, Dennis Digital-Botanic Architecture Santa Fe : SITES Books ; St. Paul,, c2005. NA2500 .D65 2005

Neil Leach, David Turnbull, Chris Williams (eds) Digital Tectonics Chichester; Hoboken, NJ: Wiley-Academy, 2004. NA2750 .D464 2004

Iannis Xenakis Formalized Music: Thought and Mathematics in Composition Stuyvesant, NY: Pendragon Press, c1992 ML3800 X24 1992

Gilles Deleuze, Félix Guattari A Thousand Plateaus: Capitalism and Schizophrenia Minneapolis : University of Minnesota Press, c1987 B77 D413 1987

Manuel De Landa A Thousand Years of Nonlinear History New York: Zone Books, 1997. Q174.8 .D43 1997

M.A.J. Chaplain, G.D. Singh, J.C. McLachlan. (eds) On Growth and Form: Spatio-temporal Pattern Formation in Biology Chichester, England ; New York : John Wiley & Sons, c1999. QH491 .O5 1999

Thompson, D'Arcy W. On Growth and Form Cambridge: University Press, 1952 QP84 T4 1952 v1, QP84 T4 1952 v2

Also take a look at the following AD issues:

-Programming Cultures: Architecture, Art and Science in the Age of Software Development (2006)
-Collective Intelligence in Design (2006)
-Emergence: Morphogenetic Design Strategies (2004)
-Techniques and Technologies in Morphogenetic Design (2006)

Pattern Formation Models

01. Biology

One of the questions that research in biology is trying to answer today concerns the very early stages of life: how from an almost homogeneous mass of dividing cells in the primal stages of development emerges the vast and sometimes spectacular array of patterns and structures observed in different forms of life. There is a continuum of different approaches to the problem (1): on the one end there are theories of preformation and on the other end systems of self organization. The concept of preformation assumes that any form is preformed and static. Therefore any new form is always a result of a combination of the already existing forms. Taking a different approach, self –organization implies a de novo pattern formation that is dynamic and gets developed over time. Morphogenesis in the self-organization model depends on the interaction between the initial cells or units. Preformation is a top-to-bottom idea, while self-orgazination is a bottom-up system. In both cases, research uses computation as the necessary medium for the simulation of the biological processes.

02. Music

The music composer and architect Iannis Xenakis in his book Formalized Music (2) divides his works -or better the methods employed in order to produce his works- into two main categories: deterministic and indeterministic models. The two categories, deriving apparently from the mathematics, are referring to the involvement or not of randomness in the compositional process. A deterministic model does not include randomness and therefore it will always produce the same output for a given starting condition. Differential equations for example tend to be deterministic. On the other hand, indeterministic or stochastic processes involve randomness, and therefore will produce different outputs each time that the process is repeated, given the same starting condition. Xenakis’ compositional inventory includes processes from both categories (3). Computation was again the main medium Xenakis used in order to apply those processes in his compositions.

03. Philosophy

In their book A Thousand Plateaus (4), French philosophers Gilles Deleuze and Felix Guattari propose a new model of organization that they call the rhizome. The idea of the rhizome is opposed to that of the tree. Rhizomatic formations resemble a network or a meshwork–like assembly where the interaction between its various elements is defining its character. Rhizomes are always dynamic and are always changing over time as a result of lack of a specific hierarchical system. On the contrary, a tree-like formation is always based on a top-bottom, strictly defined hierarchy. The internet is an example frequently used to describe a rhizomatic network. With the development of computers and global networks, Deleuze and Guattari’s ideas acquired a new meaning, and established the rhizome as one of the main theoretical tools in the study of new media and technologies.

04. Design

It is no surprise then that experimentation in the use of computational processes in architecture today is touching upon similar issues. Pattern formation models such as L-systems, cellular automata, swarm behaviors, stochastic processes etc., that are being used in various research fields, are also employed in architectural experimentation today.

Aim of the class is to explore the possibilities that the above mentioned methods are offering to architecture. How these models, deriving from biology or mathematics, can expand the architect’s inventory with new ways to organize space, with unique structural or ecological systems or with innovating techniques in form-finding. At the same time, we will try to understand how the above mentioned categories (preformation/self-organization in biology, deterministic and indeterministic in mathematics and in Xenakis work and rhizome/tree in Deleuze and Guattari’s theories) can help us approach different digital tools and evaluate the different opportunities that they offer.

The semester will be divided in two parts. During the first part the students (individually or in teams of two) will develop a research project on a specific “pattern formation model”. Through that project the student should be able to understand and analyze the model that he or she studies using advanced computational techniques (dynamics, scripting). For the second part of the semester the students are asked to use the outcome of the research project in order to develop an architectural/spatial idea.

References:

(1) Deutsch, A. & Dormann, S. Cellular Automaton Modeling of Biological Pattern Formation Boston: Birkhauser, 2004.

(2) Xenakis, I. Formalized Music: Thought and Mathematics in Composition New York: Pendragon Press, 1992.

(3) In the “deterministic” category of Xenakis’ work fall compositions like Akrata, Nomos Alpha and Nomos Gamma, while examples of the “indeterministic” approach can be found N’Shima (Brownian Motion) and Analologigues (Markov Chains).

(4) Deleuze G. & Guattari F. A Thousand Plateaus: Capitalism and Schizophrenia Minneapolis: University of Minnesota Press, 1987