FRACTAL PATTERNS IN THE BUILT ENVIRONMENT

Integrating Fractal-Based Design for Stress Reduction

by ScienceDesignLab, a collaboration between 13&9 Design and Fractals Research

What do we see in the wispy edges of clouds, in the intricate branches of trees, and in the jagged peaks of a snowy mountain range? For many years, scientists assumed these images were a haphazard mess devoid of any pattern. However, the past fifty years have seen a remarkable revolution in the way scientists study nature’s scenery, which has brought scientific inquiry and artistic views of nature closer together.

At the heart of this revolution lies the discovery of intricate patterns called fractals. Dramatically referred to as ‘the fingerprint of life’, fractals have been shown to be the basic building block of many of nature’s patterns, ranging from clouds and trees to mountains. Through 600 million years of exposure to nature’s fractals, people’s eyes have evolved to accommodate their powerful visual qualities. The ScienceDesignLab’s neuro-aesthetic experiments show that viewing fractals induces a unique interplay of positive physical and mental impacts that artificial patterns can’t replicate. This includes a remarkable reduction in stress and mental fatigue.

ScienceDesignLab at the University of Oregon © Sandra Mulder

SCIENCE DESIGN LAB

The ScienceDesignLab was formed in 2018 with the mission to create science-informed, fractal designs for application to the built environment. The lab is driven by an international collaboration between the scientific team at Fractals Research in Eugene, USA, and the design team at 13&9 Design in Graz, Austria. Together, they developed a unique software tool that crafts designs using precise scientific parameters determined by 25 years of neuroscience research. The design team creates and refines fractal patterns, which are then analyzed by the science team. The time difference between the two locations allows this iterative process to occur around-the-clock when necessary.

Dr.med.univ. Anastasija Lesjak, Prof. Richard Taylor and Arch. Martin Lesjak at the Fractal Chapel at the University Hospital in Graz © Jakob Kotzmuth

This powerful integration of art and science gives rise to fractal designs that are confirmed by psychology experiments to reduce stress, enhance cognitive skills, and promote wellbeing. Imagine stepping into a space that is guaranteed to make you feel calm and focused – a space that feels restorative. In their projects, the ScienceDesignLab shares how these intricate patterns generate such a positive experience for building occupants.

ScienceDesignLab Keynote at Neocon 2025 © Neocon

ScienceDesignLab’s fractal designs have been used by the Mohawk Group in their Relaxing Floors, Fractal Fluency and Fractal Findings collections, by Momentum Textiles and Wallcovering in their Renaturation Collection, by FACT Design in their CALM collection, and XAL Group’s xilence in their FRACTAL CODE collection. The Relaxing Floors and Fractal Fluency collections have been honored with numerous international awards.

Best of Neocon 2025 Business Impact⁠ and Innovation⁠ Award Winner © Neocon

DR.MED.UNIV. ANASTASIJA LESJAK

Dr. med. univ. Anastasija Lesjak is CEO and Creative Director of 13&9 Design, a transdisciplinary product design firm in Graz (AT) that develops projects across multiple categories such as furniture, lighting, acoustics, textiles, accessories, as well as exhibition and sound design. With her diverse background, a doctor degree at the Medical University of Graz and her product design expertise, she bridges the gap between science and use in practice as well as enhances her team’s cross-disciplinary process

Dr.med.univ. Anastasija Lesjak © Paul Micheler

As head of concepts and product development at 13&9 Design, she works with an international team of designers, scientists, universities, product developers, manufacturing partners contributing to the innovative concepts for health and well-being in the workplace, education, hospitality, public and private spaces. One of her main areas of focus concerns research into perception and the effects of specific patterns that occur in nature. These patterns have the greatest significance in the built environment, where people have little to no access to nature. From this scientific interest came the collaboration with one of the leading scientists and physicists in this field, Professor Richard Taylor from the University of Oregon and Fractals Research (USA). In 2017, they co-founded ScienceDesignLab with the mission to create science-informed, human-based fractals for application in the built environment.

Quality Choice Prize 2025 by the European Society for Quality Research (ESQR) (L-R: Dr. med. univ. Anastasija Lesjak, Presenter of ESQR, Arch. Martin Lesjak) © ESQR

In addition to her role as Creative Director of 13&9, she also consults for INNOCAD architecture. Lesjak is a frequent speaker at diverse universities and international events. She was awarded with the title “Product Designer of the Year 2019” by Interior Design Magazine (US) and has been announced as one of 13 “Industry Visionaries“ by Delve Magazine (US) in 2025.

PROF. RICHARD TAYLOR

Richard Taylor is a Professor of Physics, Psychology and Art and currently is Head of the Physics Department at the University of Oregon. He has a Ph.D. and D.Sc. in physics and a Master’s degree in art theory. He has worked in the USA, UK, Canada, Japan, Australia, Sweden, and New Zealand, has published more than 350 articles, and taught 10,000 students. This includes 11 papers in Nature and 3 in Science. In addition to his career in science, he is a trained painter and photographer. He adopts an interdisciplinary approach to studying natural patterns called fractals. His main focus is Bioinspiration – exploring the favorable properties that make fractals so prevalent in nature and applying them to artificial systems. He has studied fractals in physics, psychology, physiology, geography, architecture, and art.

Prof. Richard Taylor © Sandra Mulder

Taylor also uses his interests in nature’s patterns to encourage and promote public awareness of science-art collaborations. His work has been the subject of television documentaries (including ABC’s The Art of Science, PBS’s Hunting the Hidden Dimension, and the BBC’s The Code), many popular press articles (i.e., in The New York Times and The London Times) and magazine articles (i.e., in Scientific American, Time, The New Yorker, New Scientist and Discover).

Best of Competition 2025 Award Winner by International Interior Design Association (IIDA) (L-R: Arch. Martin Lesjak, Dr.med. univ. Anastasija Lesjak, Prof. Dr. Richard Taylor, Presenter of IIDA) © Christopher Dilts Photography

Prof. Richard Taylor regularly gives lectures around the world, hosted by organizations as diverse as the White House, the Nobel Foundation, the Royal Society and national art galleries such as the Pompidou Centre in Paris and the Guggenheim Museum in Venice. In addition to being the head of the Physics Department at the University of Oregon, he is also the director of the research company Fractals Research.

ARCH. MARTIN LESJAK

Architect Martin Lesjak co-founded Austrian-based INNOCAD architecture in 1999 and has since completed numerous projects of diverse sizes and scopes in architecture and interior design such as residential, office, hospitality, healthcare, mixed-use, educational, public, and retail. His transdisciplinary team is renowned for their “out of the box” thinking and their analytical and pragmatic approach to architecture and design by creating solutions with purpose and meaning.

Arch. Martin Lesjak © Sandra Mulder

Lesjak‘s foresight and expertise in architecture, design, and craft – as well as an affinity for art – has guided his ﬁrms in innovative directions. Together with partners, he leads multifaceted international projects combining creativity without boundaries.

In addition to many signature corporate, housing, and institutional works, current projects include an international school in King Abdullah Economic City (UAE), a competence center for MAM Health & Innovation and the first Radisson RED hotel in Vienna (AT) as well as the Fractal Chapel at the state hospital in Graz (AT).

World Architecture Festival 2025 Award ceremony (L-R: Arch. Martin Lesjak, Dr. med. univ. Anastasija Lesjak, WAF Interiors Director Nigel Coates) © WAF

Together with Dr. med. univ. Anastasija Lesjak, he founded the product design studio 13&9 Design. The award-winning firm develops concepts that take users out of their daily routines in an aim to experience personalization, creativity, innovation, well-being, biophilia, and social and environmental connectivity. The team works as a design studio for international companies developing product collections, while also operating as a label producing their own products with small-scale manufacturers, in turn supporting creative growth in their local area.

Lesjak is a frequent lecturer and speaker at several universities and worldwide events and also received one of the architecture and design community’s top honors, “Designer of the Year 2015” by Contract Magazine in the United States, followed by “Architect of the Year 2016” by BUILD Magazine in the United Kingdom. Over the years, his work has been published internationally and recognized with various awards, honors, and nominations in both architecture and interior design.

THE SCIENCE OF FRACTAL DESIGN

“My twenty five years of experiments have led to the ‘fractal fluency’ model, which declares that human vision has become fluent in the visual language of nature’s fractals and can process their features efficiently, creating an aesthetic experience accompanied by a decrease in the observer’s physiological stress-levels.”
Prof. Richard Taylor

Biophilic (‘nature-loving’) designs recognize the importance of bringing nature into the built environment. Although scientists have been studying the healing qualities of nature for more than fifty years, their experiments left a vital piece of the puzzle unsolved – what is it about nature that triggers these remarkable effects?

Taylor’s biophilic studies commenced twenty-five years ago with NASA experiments aimed at reducing astronauts’ stress-levels. His research shows that fractals are responsible for nature’s positive effects, including a 60% reduction in the observer’s stress levels. His experiments show that children as young as three years old display the same positive responses to fractals as adults, with recent experiments extending these observations down to those as young as 10 months. The ScienceDesignLab’s patterns build on this legacy with the aim of reconnecting many people of all ages with the health benefits of nature’s fractal beauty.

Phase One of the ScienceDesignLab’s designs were informed by the results of Taylor’s previous collaborations with University of Oregon psychologists, while the Phase Two designs were actively studied by these scientists. To ensure robust results, the University of Oregon experiments were replicated at the University of New South Wales in Australia.

These experiments showed that the ScienceDesignLab’s patterns balance desirable levels of preference and engagement with relaxing and refreshing qualities. The results, published in a special edition on Biophilic Design Rationale in the journal Frontiers in Psychology, show the fractal designs induce consistent positive responses across individual people in terms of their preference, engagement and refreshment, while also maintaining relaxing effects. These results suggest that the fractal pattern applications will have a positive impact on a broad range of building occupants.

Fractals are patterns that repeat at different size scales, creating shapes of rich visual complexity – some examples include clouds, branches and waves.

The branch patterns of an artificial tree repeat exactly at different magnifications (left column). In contrast, only the statistical qualities repeat for a real tree (right column). © Richard Taylor

A prevalent form of fractal – a tree – is used to highlight their intrinsic visual properties. Fractals fall into two families – exact (Image: left column) and statistical (Image: right column). Exact fractals are assembled by repeating a pattern precisely at many scales. Randomness disrupts this repetition for statistical fractals and only the pattern’s statistical qualities repeat. Statistical fractals therefore simply appear similar at different scales leading to the term self-similarity.

Exact fractals have been studied by mathematicians since the 1860s. They are scarce in nature because a small degree of randomness inevitably creeps into their patterns. Consequently, natural examples of exact fractals, such as snowflakes and romanesco broccoli, lack the cleanliness of the mathematical versions. Most of nature’s patterns are statistical fractals.

VISUAL IMPACT OF FRACTALS

Psychologists employ a parameter developed by the mathematicians to assess the visual intricacy resulting from the fractal pattern repetition. Fractal dimension D quantifies how the patterns at different size scales assemble into the fractal image projected on the eye’s retina. For simple (i.e., non-fractal) shapes, D matches what we would expect for dimension: a smooth line has a D value of 1 while a completely filled area has a value of 2. The repeating patterns embedded in a fractal line cause it to begin to occupy space. Accordingly, its D value lies between 1 and 2. When the contribution of fine structure to this fractal mix is increased, the line gradually fills in the 2-dimensional surface on the eye’s retina and the fractal’s D value therefore approaches 2.

Natural fractals with their D values: clouds, mud cracks and forests. © Richard Taylor

The low content of fine structure within the low D fractals builds a very sparse and simple shape. However, as the D values move closer to 2, the increase in fine structure content creates a much more intricate, detailed shape. Because D charts the ratio of fine to coarse structure, it measures the visual complexity produced by the repeating patterns. Behavioral research confirms that people’s perception of complexity increases with D.

To calculate the D value, the computer overlays a mesh of squares over the fractal pattern and determines the pattern characteristics based on which squares are occupied by part of the pattern and which are empty. This is repeated for different sizes of squares, allowing the computer to compare pattern characteristics at different size scales and from this comparison calculate D.

FRACTALS AND WELL-BEING

Our eyes are stimulated by this ‘fractal complexity’. Because mid-complexity fractals are the most common in natural scenery, their familiarity allows our brains to process mid-D patterns with ease. This ‘fractal fluency’ places us in a visual comfort zone that relaxes us. Fractals therefore simultaneously relax and stimulate us by amounts determined by their D values. Because of our shared evolution, all humans benefit from this neuro-aesthetic balance of stimulation and relaxation. Neurodiversity can be accommodated by selecting the D value that best optimizes this balance based on the needs of the occupants, their tasks, and the visual characteristics of the building.

fMRI studies investigate the regions of the brain used to process the visual characteristics of our fractal designs. © Richard Taylor

ScienceDesignLab’s neuro-aesthetic investigations of ‘fractal fluency’ show that the human visual system is ‘wired’ to look at fractals. Enhanced processing of fractal images takes place at multiple stages of our vision, from the eye movements used to detect fractals through to which parts of the brain are activated when ‘understanding’ them. This fractal fluency boosts cognitive engagement when people are exposed to mid-complexity fractals, particularly for visual task skills involving pattern recognition and memory.

Along with EEG studies examining brain activities, pupillography (Image left) and skin conductance measurements (Image right) quantify the stress-reductive power of our fractal designs. © Richard Taylor

When observing the fractal designs, the brain communicates with the body using the autonomic nerve system, which is known to slow heart rate and breathing, lower blood pressure, and reduce muscle tension. Using stress measurements to probe multiple body functions related to the brain, eyes, and skin, the ScienceDesignLab has shown that exposure to mid-D fractals reduces the body’s stress levels by 60%. This reduction has critical health benefits. If left unchecked, stress can impact mood (resulting in depression, anxiety disorders, and panic attacks), heart health (increasing blood pressure and decreasing nutrient absorption), gut health (decreasing immunity and triggering hormonal imbalances), and even make our skin more delicate and our joints more painful through reduced bone density.

DESIGN METHODS

The success of the design strategy lies in its supervision expertise – the combination of the “design supervision,” the “fractal supervision,” and the “manufacturing supervision” ensures that there are no weak links as the designs progress towards their completion. As with all great interdisciplinary endeavors, creativity is an emergent phenomenon beyond the capabilities of the individual teams.

The Morphing Fractals design process. Morphing Fractals create new versions of natural fractals by adapting the fractal characteristics of photographs of nature’s fractals. © ScienceDesignLab

To generate the Fractal Library of images, the ScienceDesignLab has developed two novel image generation techniques. Morphing Fractals create new versions of natural fractals by adapting the fractal characteristics of photographs of nature’s fractals. Growing Fractals create new forms of fractals that nature never got to create by allowing the computer to grow its own fractals.

The Growing Fractals design process. Fractal seeds are inserted into the landing sites of fractal flights. © ScienceDesignLab

The Growing Fractals process starts with the fractal journeys (‘fractal flights’) used by animals when they search for food. Much like a bird dropping a seed whenever it lands, the computer inserts seed patterns into each of the locations between the flights. The seed patterns are chosen and modified based on their aesthetic quality. Because the human eye also follows fractal motion, the Growing Fractal designs generate a psychological resonance with the observer.

For both Morphing Fractals and Growing Fractals, the pattern’s D value is tuned and further modifications are made to accommodate the product materials. © ScienceDesignLab

ARCHITECTURAL, INTERIOR, AND PRODUCT APPLICATIONS

Imagine a future in which designers immerse building occupants in synesthetic fractals – a “fractal atmosphere” of visual, sonic, thermal, and tactile experiences. This would induce a positive, emergent experience that people subconsciously appreciate. Manufacturers, designers, and architects have the opportunity to apply a fractal approach starting with the outside facade of a building through to the patterns on the flooring and wallcovering as well as shapes of furniture and the way they are arranged in everyday work spaces.

Occupants could walk into a room in which the fractal ceilings dampen the noise, the fractal window shades provide an optimal breeze, the fractal solar panels deliver efficient energy to the fractal lighting, and all of their patterns combine to create a stress-reducing visual environment analogous to the complex scenes of nature. In this way, fractal designs offer the potential to combine the power of aesthetics with other favorable functions.

Fractal Lighting, fractal patterns perforated on metal sheets at the Fractal Chapel at the University Hospital in Graz by INNOCAD architecture © Paul Ott

IIDA “BEST OF COMPETITION” 2025 – FRACTAL CHAPEL recognized as a pioneering project for healing architecture

INNOCAD architecture received the highest award from the International Interior Design Association (IIDA) in Chicago: the “Best of Competition” award went to the FRACTAL CHAPEL project in the University Hospital Graz, a collaboration with 13&9 Design and Fractals Research, as part of the 51st Annual Interior Design Competition. The project had previously been the category winner in the “Institutional” category. The international jury selected the project from all thewinners of the twelve categories as an outstanding example of interior design with social relevance.

Fractal Lighting, fractal patterns perforated on metal sheets at the Fractal Chapel at the University Hospital in Graz by INNOCAD architecture © Paul Ott

WORLD INTERIOR OF THE YEAR 2025 – WINNER AT THE WORLD ARCHITECTURE FESTIVAL

INNOCAD architecture‘s FRACTAL CHAPEL at the University Hospital in Graz, in collaboration with 13&9 Design and Fractals Research, was announced as the “World Interior of the Year 2025” at the World Architecture Festival (WAF) during the gala ceremony in Miami, USA. The internationally renowned festival is one of the most important competitions and meeting places for the global architecture scene. Every year, outstanding projects from over 70 countries are honored there in a multi-stage selection process.

Fractal Lighting, fractal patterns perforated on metal sheets at the Fractal Chapel at the University Hospital in Graz by INNOCAD architecture © Paul Ott

Inspired by the prevalence of light patterns in nature, fractal window blinds and fractal canopies offer further possibilities for multi-functionality. These fractal patterns can be used to obscure an unattractive view, provide shade, and cast fractal shadow patterns across a room. They can also generate a fractal breeze, providing variations in heat and air currents for the room’s occupants. Fractal shades and canopies also offer the advantage of impacting the building’s interior and exterior appearance simultaneously.

Fractal Pattern developed for a perforated floating white steel band, which not only provides sun protection but also serves as a conduit to the natural world, and offers the perforation of daylight. This dynamic fractal interplay of light and shadow movement is like the light simmering in natural fractal environments such as woods. Palliative care unit at the regional hospital, site Deutschlandsberg by INNOCAD architecture © Paul Ott

Fractal Pattern perforated on façade / shading ⁠at the palliative care unit at the regional hospital, site Deutschlandsberg by INNOCAD architecture © Paul Ott

Light fixtures can generate dynamic fractals. Dynamic fractals are common in nature and include swaying branches in the wind, flickering flames, clouds, and ripples in a river. Their movement can be expected to maintain the observer’s attention and so boost the pattern’s aesthetic impact.

Fractal Lighting, perforated fractal patterns on the ceiling with backlight at MOSH Bar & Dinner in Romania by INNOCAD architecture © Paul Ott

FRACTAL CODE for XAL Group, large-scale acoustic wall panels from recycled PET felt at XALec Headquarters in Austria by INNOCAD architecture © Paul Ott

Relaxing Floors for Mohawk Group at MAM Competence Center in Austria by INNOCAD architecture © Paul Ott

Relaxing Floors for Mohawk Group at CASA S in Austria by INNOCAD architecture © Paul Ott

Printed acoustic ceiling tiles at WAG Headquarters in Austria by INNOCAD architecture © Paul Ott

Fractal Pattern perforated on façade / shading and at custom made wall coverings ⁠at the palliative care unit at the regional hospital, site Deutschlandsberg by INNOCAD architecture © Paul Ott

FRACTAL CODE for XAL Group, large-scale acoustic wall panels from recycled PET felt at XALec Headquarters in Austria by INNOCAD architecture © Paul Ott

In an episode of Metropolis’ podcast, Deep Green, created in partnership with Momentum Textiles and Wallcovering, recorded live at NeoCon 2025 in Chicago, ScienceDesignLab discussed “Fractals: Nature’s Healing Patterns in Design.”
⁠
Editor in Chief, Avi Rajagopal sat down with Dr. Richard Taylor, whose research underpins our understanding of fractal patterns’ impact, and Anastasija and Martin Lesjak of 13&9 Design, who apply this research in their designs – including a wallcovering collection for Momentum called Renaturation Collection.⁠

LISTEN TO THE FULL EPISODE

AWARDS

SCIENTIFIC PUBLICATIONS

A Guide to Fractal Fluency: Designing Biophilic Art and Architecture to Promote Occupants’ Health and Performance

R.P. Taylor, A. Lesjak and M. Lesjak, chapter to be published in The Handbook of Neuroscience and Architecture, 2025 by Routledge

Fractal Fluency: Processing of Fractal Stimuli Across Sight, Sound, and Touch

R.P. Taylor, C. Viengkham, J.H. Smith, C. Rowland, S. Moslehi, S. Stadlober, A. Lesjak, M. Lesjak and B. Spehar, A. Di Ieva (ed.), The Fractal Geometry of the Brain, Advances in Neurobiology, 36, 907-934 (2024)

Aesthetics and Psychological Effects of Fractal Based Design

K.E. Robles, M. Roberts, C. Viengkham, J.H. Smith, C. Rowland, S. Moslehi, S. Stadlober, A. Lesjak, M. Lesjak, R.P. Taylor, B. Spehar and M.E. Sereno, Published: Frontiers in Psychology, Environmental Psychology, Research Topic “Biophilic Design Rationale: Theory, Methods, and Applications,” 12, 699962 (2021)

The Potential of Biophilic Fractal Designs to Promote Health and Performance: A Review of Experiments and Applications

R.P. Taylor, Published: Journal of Sustainability Special Issue “Architecture and Salutogenesis: Beyond Indoor Environmental Quality,” 13, 823 (2021)

Relaxing Floors: Fractal Fluency for the Built Environment

J.H. Smith, C. Rowland, S. Moslehi, R.P. Taylor, A. Lesjak, M. Lesjak, S. Stadlober, L. Lee, J. Dettmar, M. Page and J. Himes, Published: The Journal of Nonlinear Dynamics, Psychology, and Life Sciences, 24, 127-141 (2020)

WIKIPEDIA: Fractals – In creative works

WIKIPEDIA: Fractal Art – Artworks

ARCHITECTURAL PUBLICATIONS

Interior Design Magazine (US)
Metropolis Magazine (US)
Hospitality Design magazine (US)
Time Out New York (US)
Archinect (US)
Archdaily (CHL)
World Architects (US)
WA Community (US)
Visi Magazine (ZA)
Bustler (US)
INDIA ART N DESIGN (IN)
Architecture Hunter (BRA)
Parametric Architecture (US)
The Plan (IT)
Kanto (PHI)
WA Community (US)
Igloo Magazine (RO)
Die Presse Luxury Living (AUT)
Nextroom (AUT)
Contract Magazine (US)
i+D Magazine (US)
1st Look (KOR)
100 Future Objects (AT)
Interior & Sources (US)
wohninsider (AT)
Floor Trends (US)
Floor Covering Weekly (US)
Pubmed Health (US)
Buildings Magazine (US)
McMorrow Reports (US)
Around the O (US)
Archiproducts (IT)
Indesign Live (APAC)
AAHID (US)
Officeinsight (US)
formfaktor (AT)
Surface Magazine (US)
architektur.aktuell (AT)

LEGAL

All the fractal patterns are property of the ScienceDesignLab (13&9 Design and Fractals Research).

The use of the patterns is only permitted according to the license agreement. The ScienceDesignLab may terminate this agreement at any time.

Unlawful use of the patterns is prohibited.

Modification of the original graphics or using the pattern diverging from the instructions is prohibited.

Misrepresentation of authorship is prohibited, the aesthetic and stress-reductive qualities of the pattern can only be ensured after a scientific analysis performed by the ScienceDesignLab.