Aesthetic Aspects of Parametricism

July. 2015

JOAQUIM FILIPE RES. M.ARCH. PORTUGAL

AESTHETIC ASPECTS OF PARAMETRICISM preview

Some thoughts about

1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

Aesthetic values need to change “Aesthetics is a category that transcends art. Aesthetic values and sensibilities are a human universals through which we navigate both the physical and the social world. But as the social world evolves and changes and calls forth a different built environment; our aesthetic values and sensibilities need to change along with historical development. This implies the need for aesthetic revolutions as core components of paradigm shifts, or as I prefer to say: the progression of styles.”

by Patrik Schumacher. Published in: Architectuul – the blog, 23rd March 2014

1.

SYMMETRICAL CORRELATION. 1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

“The ambition is to enhance the overall sense of organic integration through intricate correlations that favour deviation amplification that make the different conditions conspicuous rather than aiming for inconspicuous compensation of different conditions. For instance, when generative components populate a surface with a subtle curvature modulation the lawful component correlation should accentuate and amplify the initial differentiation.

This might include the deliberate setting of accentuating thresholds or singularities. Thus a far richer articulation can be achieved and thus more orienting visual information can be made available.”

by Patrik Schumacher. Published in: WA (World Architecture), Parametric Design issue, Beijing 2009

1.1. Symmetrical correlations

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1.2. Symmetrical correlations

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1.3. Symmetrical correlations

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1.4. Symmetrical correlations

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2.

A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

“A discrete multiplicity is represented by space [...], It is a multiplicity of exteriority, of simultaneity, of juxtaposition, of order, of quantitative differentiation, of difference in degree; it is a numerical multiplicity, discontinuous and actual. The other type of multiplicity appears in pure duration: it is an internal multiplicity of succession, of fusion, of organization, of heterogeneity, of qualitative discrimination, or of difference in kind; it is a virtual and continuous multiplicity that cannot be reduced to numbers.”

by Deleuze, G. Published in: 2006 Design Research Society. International Conference in Lisbon

“One of the most pervasive current techniques involves populating modulated surfaces with adaptive components.Components might be constructed from multiple elements constrained/cohered by associative relations so that the overall component might sensibly adapt to various local conditions. As they populate a differentiated surface their adaptation should accentuate and amplify this differentiation.”

by Patrik Schumacher. Published in: Parametricism as Style - 11th Architecture Biennale, Venice

2.1. A Discrete Multiplicity & Continuous Dierentiation

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2.2. A Discrete Multiplicity & Continuous Dierentiation

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2.3. A Discrete Multiplicity & Continuous Dierentiation

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2.4. A Discrete Multiplicity & Continuous Dierentiation

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3.

MATHEMATICAL EVALUATION CRITERIA. 1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

Some thoughts about design process decision.

“...decompose a decision problem into its constituent parts. In its simplest form, this structure comprises a goal or focus at the topmost level, criteria [and subcriteria] at the intermediate levels, while the lowest level contains the options. Arranging all the components in a hierarchy provides an overall view of the complex relationships and helps the decision maker to assess whether the elements in each level are of the same magnitude so that they can be compared accurately.” ANALYTIC HIERARCHY PROCESS

by Thomas L. Saaty. 1995

“Making a decision implies that there are alternative choices to be considered, and in such a case we want not only to identify as many of these alternatives as possible but to choose the one that best fits with our goals, objectives, desires, values, and so on.”

by John Wang. Published in: Encyclopedia Business Analytics and Optimization

cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x) | Neovius : 3*(cos(x)+cos(y)+cos (z))+4*(cos(x)*cos(y)*cos (z)) | iWP : (cos(x)*cos(y))+(cos(y)*cos(z))+ (cos(z)*cos(x))-(cos(x)*cos(y)*cos(z)) | P W Hybrid : 10*(cos(x)*cos(y))+(cos(y)*cos(z))+(cos(z)*cos(x))-0.01*(cos(x)*cos(y)*cos(z))

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Schwarz P : -(cos(x) + cos(y) + cos(z)) | Diamond : sin(x) *sin(y) *sin(z) +sin(x) * cos(y) * cos(z) +cos(x) * sin(y) * cos(z) + cos(x) * cos(y) * sin(z) | Gyroid :

3.1. Mathematical Evaluation Criteria

sin(x) *sin(y) *sin(z) +sin(x) * cos(y) * cos(z)

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+cos(x) * sin(y) * cos(z) + cos(x) * cos(y) * sin(z)

3.2. Mathematical Evaluation Criteria

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x*sin(x)+x*cos(x)

3.3. Mathematical Evaluation Criteria

3.4. Mathematical Evaluation Criteria

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4.

THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

“The semantic layer acts as a control layer, just as the syntactic layer acts as the control layer for the semantic layer. Otherwise you get lost in abstract series [a 1 a b c 1 2 3 c 3] in no time. Its like double entry book keeping. Without it you cannot reach any complexity without getting hopelessly mired in error and confusion [...], I get the meaning layer as another correlated subsystem in my multi-system parametric model. The signifying relation is another correlation within the logic of associative modelling. Specifically, I’m taking agent-based crowd modeling as this meaning layer and program agents to be responsive to designed environmental clues in their behavior; their behavior is modulated by architectural articulation. ”

by Patrik Schumacher. Published in: Log 28, Stocktaking, Summer 2013, Anyone Corporation

4.1. The Semantic Transition of Articulated Systems

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4.2. The Semantic Transition of Articulated Systems

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4.3. The Semantic Transition of Articulated Systems

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4.4. The Semantic Transition of Articulated Systems

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5

SELF CONSISTENT AGGREGATION. 1.SYMMETRICAL CORRELATION. 2.A DISCRETE MULTIPLICITY & CONTINUOUS DIFFERENTIATION. 3.MATHEMATICAL EVALUATION CRITERIA. 4.THE SEMANTIC TRANSITION OF ARTICULATED SYSTEMS. 5. SELF CONSISTENT AGGREGATION.

“In particular, in their joint book "A Thousand Plateaus",* they develop theories of the genesis of two very important types of structures, to which they refer with the terms "strata" and "selfconsistent aggregates" [or alternatively trees and rhizomes].

Basically, strata emerge from the articulation of homogeneous elements, whereas self-consistent aggregates emerge from the articulation of heterogeneous elements as such.”

by Manuel DeLanda. Published on: On the Philosophy of Gilles Deleuzze

* A Thousand Plateaus: Capitalism and Schizophrenia - by Gilles Deleuzze & Félix Guattari

“Rather than the two-step model of double articulation, DeLanda argues that the self-consistent aggregate model involves three distinct elements. In first, heterogeneous elements, are brought together through an articulation of superpositions which establishes an interconnection of diverse but overlapping elements.”

by Jeffrey A. Bell.

Published in: Philosophy at the Edge of Chaos: Gilles Deleuze and the Philosophy of Difference

5.1. Self Consistent Aggregation

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5.2. Self Consistent Aggregation

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5.3. Self Consistent Aggregation

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5.4. Self Consistent Aggregation

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JOAQUIM FILIPE REIS. M.ARCH. PORTUGAL. JULY. 2015