INDUCTIVE PATTERN FORMATION A Dissertation by RAYMOND CHARLES MULLICAN Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of the Committee, Gabriela Campagnol Co-Chair of the Committee, Mardelle M. Shepley Committee Members, Jay R. Walton Robert K. Popp Head of Department, Robert Warden December 2017 Major Subject: Architecture Copyright 2017 Raymond Charles Mullican ABSTRACT With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete space- time model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat. ii for kaj editor-in-chief who often gives the impression of thinking this reporter has a good story If not for you The winter would hold no spring Couldn't hear a robin sing I just wouldn't have a clue, if not for you (George Harrison, 1970) thank you iii ACKNOWLEDGEMENTS 2017 College Station, Texas To Gabriela, Mardelle, Jay, and Bob: thank you. I cannot adequately express my gratitude for your kindness, thoughtfulness, encouragement, patience and amazing grace when faced with my often inarticulate meanderings, seemingly lost with only the black maps of my intuition. My ‘big six’ now stands at an even ten. Thank you also to Dean Tom Regan for offering a place to attempt this work. In over forty-five years of intermittent conversation, he always seemed to ask exactly the right question. Which, of course, was one for which I had no answer, prompting the next iteration of investigation. And to Francis Downing. If scripted by Charles Webb, Calder Willingham, and Buck Henry, the synchronicity of our last conversation would have been this single short scene: Dr. Downing: I just want to say one word to you. Just one word. Ray: Yes, ma’am. Dr. Downing: Are you listening? Ray: Yes, I am. Dr. Downing: Situated. Ray: Exactly how do you mean? One could envision a similar scene with Mark Clayton regarding the significance of proof and history. Thank you both. Every day I give thanks for my family and friends: without feeling your support this marathon would not have been possible. And underpinning it all, embedded in the probabilistic adaptive information structures of inductive truth space, thank you to the Deus ex Machina for the synchronicities of Ah-ha! moment local phase transitions that have mapped the 67 year trajectory of this pattern formation process. I’ve done my best, I know it wasn't much I couldn't feel, so I learned to touch I've told the truth, I didn't come here just to fool you And even though it all went wrong I'll stand right here before the Lord of Song With nothing; nothing on my tongue but Hallelujah. (Leonard Cohen, 1984) iv 1998 Blacksburg, Virginia Olivio Ferrari was many things to us, to me. With his memory, the meaning of one word grows ever larger as the years advance: mentor. To us all. The fabric of his weavings often revealed two common threads -- develop, then trust, your intuition, and process is ultimately larger than product. Design, as well as life, seems to be about both. Where are we? Architects were then, as they are now, interested more in the appearance of buildings than in their functioning. Witold Rybczynski “Until we have an understanding of these complicated, changing interactions, our attempts to balance extraction of ecosystem resources against sustainability will remain at best naive, at worst, disastrous. We, as humans, have become so numerous that we perforce extensively modify ecological interactions, with only vague ideas of longer range effects. Yet our wellbeing, even our survival, depends on our ability to use these systems without destroying them.” John Holland As architects we have lost or given up much of our process, as a result we have lost control of our product. We have reduced ourselves to being harbingers of fashion, with little understanding of design consequences to both the human inhabitants and a building’s extended ecosystem. Our cumbersome performance modeling tools are based on the reductionist thinking of linear relationships and are inappropriate for the analysis of architecture’s synergy. Worse, they are of little or no benefit to the creation of architecture. Revolution! Artificial life is the study of man-made systems that exhibit behaviors characteristic of natural living systems. a relatively new field employing a synthetic approach to the study of life-as-it-could be. It views life as a property of the organization of matter, rather than a property of the matter which is so organized. Christopher Langton Artificial life and the related study of complex adaptive systems [CAS] have risen from the power of computers to model the nonlinear relationships common in natural systems. Traditional science has placed emphasis on analyzing and explaining in terms of smallest parts; these are attempts to synthesize behavior and process. Self-organization and order emerge from simple-ruled, bottom-up constructions. v Towards A New Architecture Within fifty to a hundred years, a new class of organisms is likely to emerge. These organisms will be artificial in the sense that they will originally be designed by humans. However, they will reproduce, and will evolve into something other than their initial form; they will be ‘alive’ under any reasonable definition of the word. Doyne Farmer 2050: Scientific foundation of architecture. The tools of cellular automata and genetic algorithms are united with the symmetry operations of mathematical crystallography to evolve architectural morphology in computer time; to generate form in response to environmental forces - physical, social, cultural, economic. 2100: While not derived from carbon based ‘organic’ life as we know it, building assemblies will be alive in every sense -- growing, adapting, reproducing and dying in symbiosis with both inhabitants and environment. Convergence Artificial life, CAS: bottom-up, parallel processing, simple rules, emergent self-organization. Biology, economics, psychology, physics, anthropology, mathematics, art . Architecture. Déjà vu. Intuitively, we have been here before. It was called design studio. To a giant, whose shoulders were broad enough that we may all aspire to stand. Thank you. rcm, 1998 vi CONTRIBUTORS AND FUNDING SOURCES Contributors This work was supported by a dissertation committee consisting of Professors Gabriela Campagnol, advisor, and Mardelle Shepley, co-advisor, of the Department of Architecture, along with Professors Jay Walton of the Department of Mathematics and Robert Popp of the Department of Geology and Geophysics. All work conducted for the dissertation was completed independently by the author. Funding Sources Graduate study was supported by Deus Ex Machina through Federal Student Loans, the generosity of KAJ, and the kindness of strangers. vii TABLE OF CONTENTS Page ABSTRACT ......................................................................................................................................................