Fractal Matrix Architecture: Algorithmic design for environmental engagement

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Fractal matrix architecture integrates complex geometries inspired by natural systems into urban design frameworks.

Jack Oliva-Rendler is exploring work processes in digital 3D modeling, geospatial information systems (GIS), and algorithmic modeling methods for multi-scale ecological solutions at planetary, bio-regional, infrastructural, local, and community-based levels of work. Additionally, he is a tutor for the Fractal Matrix Architecture workshop, which is scheduled to take place on June 15th and 16th, 2024.

During my undergraduate studies at the Southern California Institute of Architecture (SCI-Arc) around 2015-2016, I became deeply curious about environmental architecture and technology philosophies. I reasoned that there was a deep link between our technologies and our environments, as our environments are shaped by our technologies.

I was studying information structures and the history of computation with my professors, Casey Rehm and Benjamin Bratton. There was a great culmination of my ideas in my design studio taught by my professor, Peter Martinez Zellner, when I designed a skyscraper to be like a computational instrument. Large language models (LLMs) like ChatGPT have not been popularly released, nor have any AI image-generating programs like Midjourney. I still believe that a building embedded with AI could function as a kind of environmental simulator, meaning that the building could function as a gallery, archive, and library of environmental models and visualizations. The information would flow through an aggregated structure like a synaptic nervous system throughout the vertebrae core of the tower.

I will elaborate on this concept of architecture for information systems for years. I completed a couple of thesis projects related to this in architecture school; I completed a thesis project at SCI-Arc, where I received my Bachelor’s Degree in Architecture titled “A.T.L.A.S,” and I completed my thesis “Instruments of Terrestrial Transformation” at Harvard Graduate School of Design, where I received my Master’s Degree in Architecture. Both projects were information infrastructures for Earth Observation Systems. The thesis essentially outlined a framework in which environmental data, such as remote sensing data and photography, could be aggregated spatially in libraries, galleries, and archives in building structures. The environmental information infrastructures could then function as Institutional Models where Earth Sciences and Design Disciplines could merge.

Today, at this current point in my career, in the year 2024, I have been out of school for four years. In that time, I have been blessed to explore many elaborations and explorations that relate to my thesis works that have culminated in a book titled, “Terrestrial Architecture.”

Terrestrial architecture, book by Jack Oliva-Rendler, encompasses the design and construction of buildings and structures on land, integrating environmental considerations, cultural influences, and functional requirements to create harmonious and sustainable spaces.

The workshop with PAACADEMY will focus on a certain thread throughout the book that explores prototypical abstract geometries as systems of organization and structuring. Abstract Geometrical Systems are offered to engage complex contextual scenarios in the environmental fabric. Built and natural environments are contextual for contemporary architects.

I have devoted considerable time to context modeling of urban and natural fabrics. This image, which I am sharing here, is a context model that I have developed of downtown LA. The model consists of simple massings for each building with accurate heights, while a Satellite Image is placed below the model for further contextual articulations.

Urban fabric, viewed as a cellular system, exhibits fractal geometrical patterns, fostering harmonious coexistence within built environments.

Data Layers can be added to massing models to give color-coordinated legibility for different performances in the urban environment, such as commercial space, institutional space, open space, etc. The following image shares a colored diagram of the urban context.

Urban fabrics with rich accumulated datasets are new contexts for architectural design. The metrics and formulations of dynamic phenomena representing environmental visualizations are driving variables and parameters for contemporary urban design. We are also equipped with ever more powerful computational tools that allow us to engage data-rich environmental concepts.

Data layers in urban massing models provide insights into various urban performances, facilitating informed design decisions.

Algorithms offer us a method to structure the complex fabric of our environments. We can think of the mathematization of our environments as dynamic energy systems translated into vector fields and new architectural systems designed by cellular diffusion. We can also imagine how natural systems can be translated into mathematical or parametric formulas. Plants have driving parameters to their morphological formation as they respond to variant stimuli. Parametrically 3D modeling a plant using vector fields implies many possibilities for architecture to be environmentally responsive.

Algorithms are able to generate a form in such a way that the drivers and parameters of the form influence the morphological subject matter. Possible futures of design will integrate the many variables of the environment. Ecological energy systems could drive design morphologies as buildings respond to solar angles and wind vectors – hydrological pathways and soil health maps could create opportunities for urban vegetation. As we leverage algorithmic tool sets, larger portions of urban fabric may be manipulated simultaneously as an integrated method. It is possible that we calibrate and augment our built environments as a collective entity. This could work by considering the urban fabric in clusters and aggregations. As a cellular system the urban fabric has constituent components, it is a continuous assembly of blocks and buildings. The discrete components are not autonomous members but integral role-playing agents within the urban field.

The workshop examines cellular aggregations and grid substrate subdivisions of geometry as a fractal geometrical system to aggregate volumes and lines in space. The aggregations vary in density with different senses of direction and proximity, offering modes of collective coexistence between components that may follow harmonious patterns or unified, balanced systems. Certain fractal aggregations begin to resemble ancient sacred structures like the pyramids in Egypt or Angkor Wat in Cambodia, as the elements of the design come together to form mathematically precise tapestries of tectonic aggregation.

The following image is an analysis of Angkor Wat that I worked on in graduate school in 2018 during a design studio precedent study of semiological systems with my professor, Patrik Schumacher, who was a visiting professor at Harvard GSD. An underlying geometrical system governs the schematic planning of the temple city.

Cellular aggregations in architecture resemble ancient sacred structures, reflecting precise tectonic arrangements.

Around this time, I was reading the book Godel Escher Bach by Douglas Hofstadter and familiarizing myself with the nature of fractal systems and the logic that governs their assembly. At the end of the year 2021, I discovered the software mandelbulb 3D, which opened new territories to explore fractal geometry. After 6 months of deep experimentation with Mandelbulb 3D, I was able to arrive at a city-like architecture that was fractal-based.

The model included hallways, columns, atriums, and towers, all the components of temple city architecture like Angkor Wat. However, instead of a two-dimensional abstract representation of the structure, I was able to explore a 3D model of this seemingly infinite city.

Algorithms drive the morphological formations of architectural structures, responding to dynamic environmental stimuli.

In 2023, I worked with an incredible team at Morphosis Architects for a few months. I was exposed to massive, complex Grasshopper scripts. I began rationalizing the Mandelbulb 3D fractals into more communicable and constructible forms, exploring fractal geometries using Grasshopper. I began to think of the concept of a matrix.

Information distributed in the urban fabric with address points infrastructures began making more sense as a Fractal Matrix, a storage system for energy and memories. A matrix might also define axes of freedom upon which information may traverse. The movement and storage of energy and information happen through a geometrical construct that orchestrates the composition of the matter. Our work with algorithms gives us agency in the operations that manipulate our matrix’s fabric.

Abstract geometrical systems serve as organizational tools, engaging with intricate environmental contexts within architectural compositions.

In this Fractal Matrix Architecture workshop with PAACADEMY, we will explore the depths of algorithmic design using multiple software, exploring the intricacies of Fractal Matrix Architecture. We will increase our ability to navigate and manipulate our algorithms with greater deliberate intention. With such skill sets, we may transcend complexities—we may step beyond the confines of simplistic frameworks that limit our freedoms as to what we can create.

Fractal Matrix Architecture – Studio Jack Rendler
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