gyre a serial analysis of flocking behavior and its representational tectonics PennDesign Arch 743 Research Seminar: Form & Algorithm Fall 2017 University of Pennsylvania Dept of Architecture
critics: Cecil Balmond, Ezio Blasetti student group: Sarah Davis, John Hilla, Marianne Sanche, Leetee Wang
gyre a serial analysis of flocking behavior and its representational tectonics PennDesign Arch 743 Research Seminar: Form & Algorithm Fall 2017 University of Pennsylvania Dept of Architecture critics: Cecil Balmond Ezio Blasetti student group: Sarah Davis John Hilla Marianne Sanche Leetee Wang
In mathematical modeling, flocking describes the collective behavior of selfpropelled entities. The movement of each individual entity found in a “flock� is controlled by three relational tendencies, listed below, that are responsive to the orientation of other entities in the environment. Independent control of these parameters is what allows us to manipulate the geometrically generated outputs of our model. 0.0. separation; 0.1. alignment; 0.2. cohesion Ultimately, the results of the flocking model are used as an underlying system of organization for the complex drawings that are done in the latter phases of this study. The algorithms that are used in this process will be consistent in the generation of each drawing, although the facture and representation of these base layer curves will evolve. In this way, we are able to treat the algorithm as a black box in order to arrive at conclusions about form and effect, rather than pure computationally generated results. chapter 0.0. chapter 0.1. chapter 0.2. chapter 0.3. chapter 0.4. chapter 0.5.
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chapter 0.0. flocking behavior The diagrams included in this chapter specifically show the various formal behaviors that are created from extensions of simple input curves that exist in a geometric space. Ultimately, the results of these operations are used as an underlying system of organization for the complex drawings that are done in the latter phases of this study. The algorithms that are used in this process will be consistent in the generation of each drawing, although the facture and representation of these base layer curves will evolve.
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stage 0.0. The geometric origin of this study is a series of curves that are represented in a 3-D environment. These curves are then extend by moving one endpoint a distance of one unit. In isolation, these curves are extended in the path of the original vectors. This action is elongated by increasing the number of iterations through which the single-unit extension occurs. The diagram to the left depicts a n initial series of four curves (fig 0.0.), followed by the same series after one unit of elongation (fig 0.1.).
stage 0.1. As these curves are extended further, the endpoints are repositioned in relation to the other curves in the environment. The interaction of these trails occurs when these paths pass within a variable threshold of distance from one another. In this range, the new endpoint positions leave the path of the original vector and move near the closest curve according to another order of variable conditions for cohesion and alignment. The diagrams to the left depict the early stages of this interaction.
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stage 0.2. The manipulation of the cohesion and alignment variables changes the overall behavior of the trails. fig 0.4. shows a condition of high cohesion combined with low alignment. Here, it can be seen how the trails tend to twist around the input curves, while maintaining sensitivity to the directionality of the original vectors. To the right of this, fig 0.5. is an example of low cohesion with high alignment. The endpoints in this case tend to swirl around one another in relation to their own location, not the direction of the inputs.
stage 0.3. The images to the left show a specific condition where the positions of the new points that are created as extensions of the input curves are projected on to an orthogonal plane within the XYZ coordinate system. This straightens out each step of the trail creation which results in more linear and discrete behaviors and formal effects.
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chapter 0.1. facture tectonics This chapter includes a set of drawings that are part of an investigation into the various effects derived by alternating the use of curves and their associated tangent lines as both algorithmic inputs and representational marks in a drawing. It is here that we are able to further the investigation of the algorithmic operations that have been studied in the previous chapter in order to experiment with different interpretations of curves on either side of the algorithm. In this way, we are able to treat the algorithm as a black box in order to arrive at conclusions about form and effect, rather than pure computationally generated results.
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stage 0.0. The diagrams to the left show a self-similar set of potential algorithmic inputs that can be represented as either geometric curves (fig 0.0.) and/or tangent lines (fig 0.1.). These curves are arranged close to one another in a symmetrical pattern, as such a condition will provide an ideal environment for the interactions between curves that were derived from the same algorithms that were used in the previous catalog of diagrams.
stage 0.1. In the set of diagrams here, we see the results of using tangent lines, rather than the curves themselves, as inputs to our algorithm. fig 0.2. is the direct result of this, while fig 0.3. is a second level of this investigation which reinterprets this output also as tangent lines. One notable difference between these two drawings is that the original output is composed of smooth curves, while the reinterpretation converts this to a similar form made entirely of straight lines.
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stage 0.2. The diagram in fig 0.4. layers the resultant curves on top of their tangent lines. fig 0.5. then builds on this by looping the original input curves back into the algorithm. This reinstates these curves as elements that need to be responded to after the algorithm has run. With this new addition, we can begin to experiment more by using other curves found in the drawing as second order inputs to the algorithm.
stage 0.3. The case on the left shows the results of the same algorithm used above where the resultant curves have replaced the input curves as second order condition in the geometric environment. This is complimented by the diagram in fig 0.7. which experiments with the tangent lines used in that position. The formal and effective qualities of this particularly series proposes the best opportunities for sequential and iterative studies performed by varying the simple numeric variables in the algorithm.
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chapter 0.2. variable alignment sequence This chapter is dedicated to a sequence of drawings that show the formal results that are generated by mathematically increasing the weighted impact of the alignment variable, while all other variables are held constant. Here, it can be seen that when alignment has a greater impact on the overall behavior of the flock, the endpoints of each curve entity tend to swirl around one another with relation to their own location, not the direction of the inputs themselves.
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chapter 0.3. variable cohesion sequence This chapter is dedicated to a sequence of drawings that show the formal results that are generated by mathematically increasing the weighted impact of the cohesion variable, while all other variables are held constant. Here, it can be seen that when cohesion variable has a greater impact on the overall behavior of the flock, the trails tend to twist around the input curves, while maintaining sensitivity to the directionality of the original vectors.
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chapter 0.4. breaking symmetry The entirety of this study is done using a symmetrical set of input curves that are manipulated as a group using identical variables. It would logically follow that the output of such a system would also be symmetrical, but as the following set of drawings will reveal, the separation variable of flocking behavior creates anomalous tendencies for breaking symmetrical underpinnings. The set shown in this chapter depict a specific case of this movement towards asymmetry by means of separation.
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chapter 0.5. field drawings The drawings that result from the established algorithms and processes contain a broad variety of different behaviors of lines that extend and move around one another. By zooming in on specific moments of these phenomena, we start to investigate and compare new effects and patterns that emerge at various scales and perspectives. This action also allow us to evaluate the ability of these small resultant moments to fill a field and how this elimination of boundaries open us to new inferences about the power of our generative algorithms.
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