Accessing Nature’s Fractals in Urban Environments for Meditation

Research and prototyping sprint at Biodesign Studio, RISD

Our society has largely conformed to the advancements brought by the scientific revolution of the 1500s, with developmental leaps in mathematics, physics, biology, astronomy and chemistry — transforming the views about how nature works and changing our present lives. Although written records of human history only go back to 5000 years, through findings and consensus we know that our species has inhabited earth for millions of years, evolving in a nature-centric manner as part of a complex biological system. A few months ago, Homosapien remains from 315,000 years ago were found in Morocco, pushing back our origins by 100,000 years. Our anatomy has remained relatively the same since then, and yet our lives are completely different.

What sets humans apart from other sentient animals is the enhanced ability to think, learn, gather and pass on knowledge. It may be incoherent to compare our intelligence with animals since they have instincts and senses that go far beyond our capabilities. Dogs for instance have up to 300,000 million receptors in their noses compared to about 6 million in us, giving them an incredible sense of smell that is now being used to diagnose diseases including cancer. A team of scientists and Andreas Mershin at MIT and Harvard are developing a rival olfactory device that can detect and analyze trace molecules. In a recent Biodesign Studio class at the Rhode Island School of Design, Mershin described this technology as “a soon to come reality through personal devices like smartphones having miniature sensors that detect diseases”. Similarly, through this study, I aim to observe nature’s underlying forms and processes and apply them to healthcare solutions.

We are affected by a magnitude of problems, particularly felt in urban areas due to high congestion and pollution. Through the agricultural, industrial and information revolution, our species has succumbed to a variety of unnatural lifestyle choices in food, apparel, electronics and long lists of consumer items. Coupled with COVID-19, a global study found over 70% of participants had greater than moderate stress and 59% had clinical anxiety. Ironically, mental health solutions are also constantly advertised as products and services, confusing people further.

Meditation by Nature

Looking through the lens of stress management, biophilia is an evolutionary experience and is only beginning to be scientifically explored. It was introduced in 1984 by Edward Wilson in a volume called ‘Love of Life’ and describes an innate emotional affiliation of human beings to other living organisms, or being in nature. A recent article from The Washington Post resurrected words from Wilson with contrast to the urgency of mediations on earth’s fragility.

Using biophilia as a medium for stimulus, we can gather benefits that improve self-awareness and creativity, extend flow states and increase overall performance. We can craft experiences based on nature that aid neural activity, act as a medium for palliative care in terminal illness and address various mental health problems including PTSD, anxiety and depression. Additionally, physiological benefits include reduced blood pressure levels, pain relief and improved disease recovery.

The brain has the potential to develop neural connections triggered by adaptations in how we perceive and interact with nature. One example is the five basic senses encompassing sight, hearing, touch, smell and taste. About the stimuli, we have simplified sensory adaptations as synesthesia, enhancement and deprivation.

  • Synesthesia: Synesthesia is a phenomenon where areas of the brain are responsible for different senses are exchanging information. It’s found in 2–4% of humans where the pathways allow them to visualize sound, smell colors and more.
  • Enhancement: To focus senses and extend the threshold of sensory awareness, practices have been around for thousands of years from religious traditions and rituals using the elements (fire, water, earth, air and space) to chants, actions and entheogens that enhance sensory effects. This includes meditative practices such as Vipassana, Zen and Mantra.
  • Deprivation: By diminishing the source or blocking stimulus, traditional methods include fasting, sleep deprivation and isolation. Modern techniques include sensory deprivation tanks where you’re suspended floating in body-temperature water within a dark sound-proof chamber.

There is a complex interrelationship between sensory adaptations and brain waves. However, through historical and now scientific evidence we know that entering an altered state corresponding to brain wave frequency shifts is not only possible but can have profound effects. Biophilia may a low-cost and low-risk method of achieving the desired neural activity.

Brain Waves

The four lobes of the brain are responsible for cognitive functions, processing sensory information and much more. Over the last few decades, advancements in neuroscience and neurobiology have improved our understanding of the brain and its functions, properties of which have been applied successfully across domains of medicine, mixed-realities, robotics, education and more. Two common techniques in brain scanning are Functional Magnetic Resonance Imaging (fMRI) can capture the flow of blood volume and oxygen and highlights areas responsible for various mental states. The second is Electroencephalography (EEG) which detects neural activity and changes in brain waves, categorized by the frequency range.

  • Delta waves (0. 5 to 3 Hz) — The slowest recorded waves in humans, Delta waves are found in infants, associated with deep levels of relaxation, restoration and healing.
  • Theta waves (3 to 8 Hz) — Theta brainwaves occur most often in adult sleep but are also dominant in deep meditation. It mediates learning, memory and higher understanding.
  • Alpha waves (8 to 12 Hz) — Alpha waves occur in wakeful relaxation and meditation, some of the positive effects of boosting alpha waves include lowering stress and improving creative thinking.
  • Beta waves (12 to 38 Hz) — Commonly observed when awake, Beta waves are involved with conscious thought and logical thinking.
  • Gamma waves (38 to 42 Hz) — Fastest recorded brainwaves, these make the brain highly alert and conscious, improving problem-solving abilities.

So how does being in nature affect brain waves?

The Fractal Universe

Fractals are a fascinating reality. We see them everywhere — from neurons in the brain to spirals of galaxies. Observed nature lies in various levels of magnitude within a fractal-based system that can be mathematically and geometrically modelled. Using the science of fractals to understand nature’s processes, we can predict natural phenomena and prepare solutions. The interpretation of the world is simplified by the human perception into simple geometric shapes, but the scales of magnitude in nature are extensive and nature’s growth follows fractal patterns. This means, for example, even minor disturbances in airflow or solar heating, the weather might change geometrically with time. In the 1980s Benoit Mandelbrot popularized the concept of fractals, using an IBM computer to generate these complex geometries with simple mathematical functions. Since then, the unique properties of fractals have been used across modern science and technology. Representing the universe with considerations in fractal geometry is more accurate but can also be difficult to measure. However, this unperceived complexity in nature’s forms and processes is receding as a new era of awareness and predictability approaches, using new tools to visualize and process fractal-based design. There is considerable discussion about fractals being the building blocks of the universe.

The math behind fractal dimensions using Sierpinski Triangle as an example

The next phase of my research funneled through fractals and their mathematical and health properties. Fractal patterns in nature are evidenced to be directly responsible for positive stimulation in human neural activity. People who lived in areas close to nature had healthier bodies. The majority of people, including those I spoke to, enjoy spending time in nature and feel consistent improvements in mood. Although the science behind fractals is still being discovered, some studies suggest that fractals possess visual properties that aid sensory adaptions and health.

  • Our immune mechanism is reinforced and stress levels are reduced in biophilic environments (Salingaros, 2019).
  • There is a significant correlation between living near nature and healthy brain structure (Kuhn, 2017) and improved mental health (Bratman, 2019; Preuss, 2019).
  • Fractal patterns found in nature are directly responsible for the positive stimulation of human neural activity (Terrapin, 2012)
EEG test of watching fractals in a carboard prototype VR

To learn about the brain in digital biophilia and how we may control brain waves, the participant (me) watched fractal patterns of nature and procedural models rendered as images or 360 videos. Comparative experiment insights from four test cases are used to validate the mental health effects of fractal visualization and design healthcare solutions based on fractal geometry in physical or digital environments. The objective of this study was open to interpret the effect of different visualization types. It was hoped that certain fractal environments would produce relatively lower frequency brain waves — Delta (0.5–3Hz), Theta (3–8Hz) or Alpha (8–12Hz), as compared to the baseline at Beta (12–38Hz).

Fractal images extracted from Google Earth, Himalayan Range

Electroencephalography is used to analyze the waves in four case studies. Neural activity is measured on one participant in the 4 fractal visualization cases. 30-second brain wave samples from this were studied for changes in the frontal lobe sensors, observing wave characteristics such as Continuity (synchronization) measured in time of steady amplitude, Frequency (relaxation) measured in cycles per second, and Amplitude (intensity) measured in deviation.

Brain waves at the frontal lobe while fractal patterns are visualized in natural (1) and digital environments

Surprisingly, physical fractals in nature improved continuity but were only slightly better than the baseline, possibly due to environmental disturbances and discomfort. And interestingly, we see that fractals watched in digital environments improved the average quality of continuity, amplitude and frequency. Two of these — procedural fractals and 360⁰ videos (VR) shifted into the Alpha wave spectrum which is associated with lowering stress, reducing anxiety and depression, and improving creative thinking.

View the detailed case studies and recordings here.

For those living in urban spaces, access to nature can be challenging and depends on proximity, weather and a range of unpredictable external factors. There is a need for biophilic access for those who are unable to physically experience earth’s elements and its fractal properties. We spend the majority of our time indoors, looking at flat walls and rectangular objects. The potential device would take people into new dimensions to watch something the human eye has evolved to see. From this study, watching fractal geometries in digital and virtual reality was equally or more effective in tuning brain waves for stress reduction. Some methods such as procedural models and VR performed better for producing Alpha waves, which can address physiological and psychological health concerns. I believe combining procedurally modeled fractals in immersive experiences would yield Alpha waves with even longer continuity, which is the neural activity found in flow states. VR technology coupled with fractal mathematics and computer modeling may be a new frontier for biophilia and fractal immersion, expanding the scope in remote treatment and therapy, as well as consumer products and personal use.

With a vision of immersive fractal meditation, the hardware is currently under construction for further tests. There’s tons of scope in interaction design, medical procedures, product engineering and its impact on the ecosystem. This includes using open-source software such as Blender for designing and 3D modeling virtual fractal environments. Moreover, the rendered environments can be optimized for computation using fractal surfaces and ray-marching technology. Additional frameworks would be needed for prolonged use and safety. Finally, spatial audio, soundscapes, eye tracking, sensors and feedback in mixed reality can be used to deliver rich interactions within the altered state of consciousness, supporting nervous system monitoring, and personalized health experiences.

I’d like to thank everyone who gave me a constant flow of ideas and encouragement in this bizarre experiment that led to exciting results: Peter Dean, Charlotte McCurdy, Andy Law, Tim Maly, Sarah Alix Mann, Jared Mompoint, Saakshi Kale, Rini Singhi, Shravan Rao and everyone from my studio cohort.

Thanks for reading!

-Arvind Bhallamudi



Arvind is a design engineer Mastering Industrial Design at RISD, investigating green products and systems at the intersection of healthcare and sustainability.

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Arvind Bhallamudi

Arvind is a design engineer Mastering Industrial Design at RISD, investigating green products and systems at the intersection of healthcare and sustainability.