WORKING WITH FRACTALS A RESOURCE FOR PRACTITIONERS OF BIOPHILIC DESIGN A PROJECT OF THE EUROPEAN ‘COST RESTORE ACTION’ PREPARED BY RITA TROMBIN IN COLLABORATION WITH ACKNOWLEDGEMENTS This toolkit is the result of a joint effort between Terrapin Bright Green, Cost RESTORE Action (REthinking Sustainability TOwards a Regenerative Economy), EURAC Research, International Living Future Institute, Living Future Europe and many other partners, including industry professionals and academics. AUTHOR Rita Trombin SUPERVISOR & EDITOR Catherine O. Ryan CONTRIBUTORS Belal Abboushi, Pacific Northwest National Laboratory (PNNL) Luca Baraldo, COOKFOX Architects DCP Bethany Borel, COOKFOX Architects DCP Bill Browning, Terrapin Bright Green Judith Heerwagen, University of Washington Giammarco Nalin, Goethe Universität Kari Pei, Interface Nikos Salingaros, University of Texas at San Antonio Catherine Stolarski, Catherine Stolarski Design Richard Taylor, University of Oregon Dakota Walker, Terrapin Bright Green Emily Winer, International Well Building Institute CITATION Rita Trombin, ‘Working with fractals: a resource for practitioners of biophilic design’. Report, Terrapin Bright Green: New York, 31 December 2020. Revised January 2021 © 2020 Terrapin Bright Green LLC For inquiries: [email protected] or [email protected] COVER DESIGN: Catherine O. Ryan COVER IMAGES: Ice crystals (snow-603675) by Quartzla from Pixabay; fractal gasket snowflake by Catherine Stolarski Design. 2 Working with Fractals: A Toolkit © 2020 Terrapin Bright Green LLC OVERVIEW The unique trademark of nature to make complexity comprehensible is underpinned by fractal patterns – self-similar patterns over a range of magnification scales – that apply to virtually any domain of life. For the design of built environment, fractal patterns may present opportunities to positively impact human perception, health, cognitive performance, emotions and stress. Yet, designing with fractals can also come with implementation challenges. In 2014, Terrapin Bright Green classified fractals under the biophilic design pattern ‘Complexity and Order’, as to indicate “rich sensory information that adheres to a spatial hierarchy similar to those encountered in nature”. Today we recognize that fractals, can span beyond a single pattern to help characterize form, light, sound, and even spatial characteristics. With the recent surge of interest in fractal geometries – both among peer-reviewed research outputs and as a particularly accessible design attribute for architects and interior designers – Terrapin identified the need for a design-oriented document addressing key learning points for design practitioners interested in working with fractals. Significant research insights can take an average of 17 years before making it into industry practice. As a joint effort between Terrapin, Cost RESTORE Action, Eurac Research, International Living Future Institute, this project aims help shorten that gap. By identifying the most appropriate data and resources, this work hopes to advance the understanding and discussion of fractals for direct application by the design community and related sectors and industries. This paper focuses on the research and design opportunities supporting the visual experience of fractals for the indoor environment. The aim of this paper (PART 1) and toolkit (PART 2) is to: • Appreciate the value of fractal patterns and incorporate them within their projects. • Illustrate that nature-based fractal patterns can lead to significant positive health benefits. • Encourage product and material selection featuring fractal patterns to optimise associated health benefits. PART 1: FOR THE LOVE OF FRACTALS THE HISTORY AND SCIENCE OF FRACTALS FOR INDOOR ENVIRONMENTAL HEALTH PART 2: WORKING WITH FRACTALS A TOOLKIT FOR DESIGNERS 3 Working with Fractals: A Toolkit © 2020 Terrapin Bright Green LLC PART 1 FOR THE LOVE OF FRACTALS THE HISTORY AND SCIENCE OF FRACTALS FOR INDOOR ENVIRONMENTAL HEALTH FRACTAL FLUENCY, A TRADEMARK OF NATURE FRACTAL DESIGN, ARCHITECTURE AND ART What is perhaps most intriguing is that the appeal IN HUMAN HISTORY of fractals is potentially innate and not learned, as adult-like preferences for fractals have been detected Fractals have permeated cultures spanning across in urban-raised children as young as three years old many centuries and continents, classical art and (Robles et al., 2020). vernacular architecture from the column capitals of ancient Greece, Egyptian, Aztec, Incan civilisations, the art of Ancient Mayans, Islamic and Hindu temples, FRACTALS AS NATURAL PHENOMENA Angkor Wat in Cambodia, the Eiffel Tower in Paris, and Nature is characterized by a particular type of statistical the structures of Santiago Calatrava. Fractals are also geometry, different from Euclidean geometry, called evident in such well known works as those of Botticelli, fractal geometry (Mandelbrot, 1982). Humans evolved in Vincent van Gogh, and Jackson Pollock. Their visual complex and sensory rich natural environments, where all properties were also explored by mathematicians of natural structure are fractals on a hierarchy of scales, when Benoit Mandelbrot published The Fractal from the large to the microscopic. At present, the majority Geometry of Nature (1982) in which he catalogued of global population live in built urban environments nature’s statistical fractals and discussed them using characterised by minimalist/Euclidian architecture (e.g., mathematical methods for their replication. straight lines, right angles, empty planes, rectangles, Fractals constitute a central component of human cubes, cylinders, etc.) resulting in spaces that do not daily experience of the environment (Taylor & Spehar, adequately nurture and revitalise. Abundant research in 2016). While extensive research has documented the environmental psychology suggests that humans need negative effects of environments that do not have fractal scales, rich patterning, spatial layering, and a complement of rich experiential aesthetic variety interlocking geometries that are typical of nature. From (Mehaffy & Salingaros, 2013), their proliferation in an evolutionary standpoint we could venture to surmise art and design has continued to grow and diversify, that humans are instinctively drawn to fractal features creating architecture, interiors and products designed for their survival value. Within a contemporary context, a for human needs (Taylor & Spehar, 2016). Over good habitat is one in which people can function at their the past two decades, interdisciplinary teams have optimal potential (Kellert & Calabrese, 2015); thus, when confirmed that the aesthetic qualities of nature’s nature’s trademark for complexity and order is applied fractal patterns can induce striking effects on health.1 to architecture and design, restorative, nourishing and satisfying spaces, products and materials result. 4 Working with Fractals: For the Love of Fractals © 2020 Terrapin Bright Green LLC ENTOMOLOGY & TAXONOMY WHY PEOPLE NEED FRACTALS DEFINING FRACTALS FRACTAL FLUENCY, HEALTH AND THE ALLURE OF NATURAL GEOMETRIES The term fractal comes from the Latin fraˉctus, meaning ‘broken’ and ‘to break, shatter’. The French The experience of fractals has quantifiable health mathematician Benoit Mandelbrot (1924–2010) benefits, including reduced stress, improved cognitive coined this term as a means to describe a ‘never- functioning, enhanced creativity and problem solving, ending pattern’ ubiquitous in nature. The term was heightened appreciation for nature and positive suggested in Mandelbrot’s 1967 book How Long is emotions (see table 3). The benefits of fractals the Coast of Britain: Statistical Self-Similarity and specifically, and of nature more generally, have been Fractional Dimension, and indicates the consecutive shown to occur within minutes, even seconds (Smith magnifications of self-similar patterns. et al., 2020; Lee et al., 2015). As people increasingly find themselves surrounded by urban landscapes, Fractals are self-similar patterns over a range of they become disconnected from nature’s fractals and magnification scales (Fairbanks & Taylor, 2011; its stress-reduction qualities. This nature deficit can Mandelbrot, 1983), resulting in visual stimuli that lead to an unhealthy build-up of stress and the sense are inherently complex and organised. A fractal of placelessness. dimension, abbreviated as ‘D’, is the parameter that indicates fractal complexity or the scaling hierarchy Prolonged stress mobilisation in humans produces a between the patterns at different magnifications. This plethora of harmful consequences, such as increased D value lies across a range from 1.1 to 1.9, with D=1 blood pressure, energy depletion, heightened release and D=2 indicating no fractal properties. For example, of stress hormones, decreased cognitive ability, a smooth line (containing no fractal structure) has and reduced immune function. The World Health a D value of 1, while a completely filled area (also Organization declared stress to be the “Health epidemic containing no fractal structure) has a D value of 2. of the 21st Century” with associated illnesses ranging from depression to schizophrenia (Smith, 2012). Stress- STATISTICAL AND EXACT FRACTALS related illnesses cost countries such as the US over $300 billion (€267.3 billion; £242.4 billion) annually Given the prevalence and variety of fractal patterns (Taylor & Spehar, 2016). In the UK, poor mental health across nature, art and science, this paper focuses costs employers up