Pattern Explorations & Reaction-Diffusion Models

Oct 7, 2016 · 8 min read


As I began to transition from color analysis to pattern analysis, an interesting work was brought to my attention. In Kouhei Nakama’s production, Diffusion, programming is used to generate patterns on a human form. THe central question of the piece is “Why do humans not have patterned skin like animals?”. To explore this concept, Nakama implements reaction-diffusion algorithms to generate patterns that resemble those found in plants and animals. I found this piece incredibly inspiring and decided to look into reaction-diffusion further.

Kouhei Nakama’s piece, DIFFUSION

Algorithms in Nature

I began reading more about reaction-diffusion, particularly as it pertains to animal patterning. First, I read “Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation,” by Shigeri London and Takeshita Miura.

The study investigates reaction-diffusion models as they may pertain to the development of self-regulating pattern formation in vertebrates. The article shows how these patterns, also called Turing patterns, are exhibited in various species and details how they are able to be expressed and dynamically adjusted.

In regards to my research, a section on pigment interactions and resulting pattern formation in Zebrafish lends itself well to improving my understanding of how and why these patterns present themselves in Poison Dart Frogs.

In particular, I learned that these interactions tend to occur between two pigments, which validates my findings around the dyad-based organization of pigments in the frogs. Additionally, the ability of these patterns to be predicted by algorithms means that I can generate a near infinite number patterns for the cycling gear prototypes, making it possible for a cyclist to easily customize their gear to represent their cyclist identity.

Key findings:

  • Reaction-diffusion patterns, also called Turing patterns, occur as an interaction between two types of pigmentation cells; thus, it makes sense that the frogs exhibit various color dyads, even when more than two colors are present, backing up my findings and rule-making from my color analysis of the dart frogs
  • Article led me to the original article on reaction-diffusion patterning that was published by Turing in 1952, which I can use to better understand the algorithms behind these patterns so I may create a generator of the patterns — related to customizability of the cycling gear.
  • The article also led me to a simple generator of RD patterns that I can play around with by altering the parameters of the algorithms used.

Given the finding that an algorithm and some programming could create these patterns, I began looking into platforms that are already implementing a similar, algorithm-based customizer for wearables and found this interesting site:

The site invites you to create your own fashion design by asking a few questions regarding your demographics, taste in art, and mood and having you draw something on the screen. From that information, it generates a design for you and tells you about the sources of inspiration. (It also is definitely feeding your data to the creators…) While I don’t see this machine learning aspect as being entirely relevant to my research goals, I do find the concept of a site that allows a person to design their personal pattern intriguing. If someone could set certain variables (i.e. palette, mood, tastes) that then set the parameters of a reaction-diffusion model, a person regardless of their programming skills would be able to start generating patterns and color combinations that are meaningful to them while ensuring that the basic concepts are set for the characteristics that increase safety.

Before I jumped into the digital realm, I wanted to understand these patterns further through analog means, so I started drawing some frogs and trying to figure out what the rule would be for developing their various patterns.

Additionally, I wanted to read the basis for the Reaction-diffusion article, The Chemical Basis of Morphogenesis by Alan Turing. While not of the article pertained to skin patterning and it was fairly mathematics heavy in content, the parts that were relevant were enlightening. Luckily, I have a pretty decent mathematics background so I could translate the formulas and derivations into a key takeaway regarding pattern diffusion:

  • Reaction-diffusion patterns manifest as a result of the diffusion of energy possessed by the various pigment chemicals — less energetic pigments giving way to the more energetic ones until final patterns are relatively established. The types of patterns then depend on the chemical basis of the pigments

While this exploration does not inherently effect the outcome of my project, I feel that I must fully understand a phenomena before I can start using it for another objective. Plus, I’m really interested in the work of Turing and his developments in the field of mathematics, so finding out he was influential in a core part of my research was very exciting.

Biofluorescence Patterning as Communication

Another issue I need to explore more is how time of day affects cycling safety. While I think people assume that after dark would be the most dangerous time to ride your bike, I have always found nighttime to be the least stressful time. I have multiple lights on my bike and there are fewer cars on the road at that time of day. Weekend nights do present a certain danger as the likelihood of encountering driver who have been drink are probably higher. Overall, I like riding at night better than during the day. There’s a certain feeling of freedom that comes with flying around the city at night. Something I’ve always enjoyed about riding a bike is the speed at which one can travel. It’s faster than walking, but not so fast that you miss out on interesting, little moments happening in the environment. You get to see the city in a completely different way.

Blurry city lights and happy fish

So I decided to investigate the cycling fatality data based on time of day and found that the time that presents the most danger to cyclists is between the hours of 6pm and 9pm with 20% of all cyclist fatalities.

This makes some sense given that, generally, that is the point in the day when the light is changing the most. It’s important to recognize that these data are also including fatalities that were not caused by a cyclist-motorist encounter, such as rider inattention or poor infrastructure (i.e. potholes). Granted it also seems to be the case that weekday rush hour (between 3pm and 5pm) is pretty dangerous too, but probably that is due to driver (mis)behavior and impatience, which I’m considering to be outside the scope of my project. Making people be more patient is too grand a plan for a Master’s thesis.

In keeping with the theme of biomimicry, I asked myself, how do other animals handle the issue of poor lighting? In my explorations, I came across the incredible and under-appreciated catshark, specifically the chain catshark and swellshark species.

Chain catshark (left) and Swellshark (right)

While the chain catshark prefers the Atlantic and the swellshark, the Pacific, both of these small shark species are native to deep coastal waters around the Americas. Dwelling at a depth of 1,600 to 2,00o feet, sunlight is limited — They exist in a world illuminated by only blue light. As a result, they have developed an adaptation in their skin pigmentation that lets them use their limited light to their advantage. These sharks have a pigment that absorbs this particular frequency of blue light and re-emits it as a green color of light, creating incredible patterns across their skin. This process is called biofluorescence and it is different from bioluminescence as the organism is not chemically producing its own light. What is particularly interesting about this type of light emittance is that it is only visible to other sharks.

Showing the various skin patterning and illuminated forms

These sharks’ eyes are specially designed to exist in this extreme environment. They have very long rods which help them to see in extremely dim light, but their color vision only encompasses the green to blue spectrum. It is still undetermined whether larger sharks, predators of these species, or the prey of the catsharks have the same vision capabilities; however, it is clear these organisms are, at the very least, communicating with each other by standing out from the background of their blue world. Furthermore, they seem to have control over degree to which they emit this green light, increasing both the brightness and the contrast of their skin patterns as they descend into deeper water. For more on these crazy creatures check out the National Geographic article.

Returning to the world of humans and bicycles, how can we co-opt this amazing strategy for communication in darkness and apply it to the gear of cyclist riding in dimming light? It is interesting to note that once again contrast, when illuminated, is the key to the effectiveness of these patterns. Additionally, these patterns are using color and pattern designed around the visual perception capabilities of their species.


Written by


Designer. Anthropologist. Cyclist. Hiker.

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