What is Parametric Architecture and How is it Connected to Health?

Overview: In this article, we’re going to discuss the topic of Parametric Architecture, Parametric Design or Parametricism, and the many definitions relative to the proliferation of these designs in the 21st century. We’re specifically going to discuss the possible connections between these designs and health, and explore what these connections might be relative to the topic of Architectural Medicine.

While Parametric Architecture or Parametric Design is not new, there has been a tremendous increase in architectural designs around the world of this design style in the past twenty years.

While there is much discussion and differing viewpoints on the definition of Parametric Architecture, by providing some history of this topic along with past and current developments, we’ll delve into this subject and explore this important topic for the built environment in the 21st century.

Parametric Architecture or Curving Architecture

To start with, there are a few different labels discussing this topic, from Parametric Architecture and Parametric Design, to Parametricism. The first two have practically the same overlap in definition, with Parametric Architecture often listed as a segment of Parametric Design. [2] the word Parametricism has its own distinct, yet similar definition that we will also explore later in this article.

The simple definition of parametric design is shapes and forms that have a curving nature, often similar to a parabola or other flowing forms in the shape of arcs. These forms can include the arcs of entryways, or the entire shape of the structure can be in the form of flowing curves. Good examples of these types of designs are the TWA Building and the Ingalls Rink at Yale both by Eero Saarinen. The works of Antoni Gaudi and the current-day designs of Frank Gehry’s Guggenheim in Bilbao Spain are other good examples of these designs. As the saying goes, an image is worth a thousand words, so below are images that show these distinct forms with curves and arcs that are atypical of the box-like, rectangular forms of most buildings.

The work of Antoni Gaudi can be seen as an early example of designs based on these types of curves, which can be graphed based on a set of “parameters”, much like a parabola or other conical cross-section would create. And while Gaudi may not have used the mathematical approach to achieve these shapes, he did create the forms of Sagrada Familia based on the catenary curve by hanging chains from the ceiling of his design studio to determine his designs. By using these hanging chains, he then inverted these arcs to define his designs, and essentially based these shapes as a physical connotation to the mathematical equivalent of these parameters.

In the mid-20th century, designers and engineers, such as Frei Otto, would create these curving designs by utilizing mathematical equations as “parameters” to engineer these curves and forms.

Parametric Design – First Look – Just the Math

The term “parameter” is a key term to this design approach. The use of the word parameter in this sense of design can be based on the mathematical “Parameter”, which can be defined as, “in mathematics, a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation.” [3] If you’re a math professional or advocate, this definition may make perfect sense, yet for others, this can be fuzzy as to what exactly this means.

What this is essentially defining is a curving line or form.

It is essentially an arc that is defined by a set of parameters, or numbers, whose shapes can be defined in an equation.

This is particularly important if you are to use a computer to define and engineer these shapes. And in modern day computing, along with modern-day CAD programs, these curves and forms can now be graphed into forms that can be shown in three dimensions as architectural forms.

The ability to utilize these software applications also allows the engineering of these forms to be evaluated and equated, so that these CAD drawings can also be fabricated using CAE and CAM.

The ability to design, manufacture and fabricate these forms using the computer, is likely a big reason why there are so many more architectural designs using these curving forms in modern-day time. In the past, the amount of manual labor that would be required to both engineer and manufacture these shapes into steel, aluminum and other materials would be cost prohibitive.

The computing factor is actually an important topic related to parametric design, due to these forms being created on computers as opposed to drawings and various experiments that were done by Gaudi and other designers in the pre-computer time. And this is the reason why Parametric Design has often become synonymous with mathematics as algorithms, as opposed to many historical designs that were hand drawn.

This viewpoint is, in my opinion, a short sided view of parametric design, and I discuss these thoughts later in this writing.

A Deeper Dive into the Math

(If you don’t have an interest in a deeper dive into the Math, you can skip to the next section below)

So to help bring more clarity and depth to this topic, let’s explore two other definitions related to Parametric Design based on Analytic Geometry and Mathematical Analysis from Wikipedia on Parameters:

Analytic Geometry: In analytic geometry, curves are often given as the image of some function. The argument of the function is invariably called “the parameter”. A circle of radius 1 centered at the origin can be specified in more than one form:

    • implicit form, the curve is all points (x,y) that satisfy the relation (x^{2}+y^{2}=1)
    • parametric form, the curve is all points (cos(t), sin(t)), when t varies over some set of values, like [0, 2π), or (-∞,∞): (x,y)=(\cos \;t,\sin \;t)
where t is the parameter.

Hence these equations, which might be called functions elsewhere are in analytic geometry characterized as parametric equations and the independent variables are considered as parameters.

Mathematical Analysis: In mathematical analysis, integrals dependent on a parameter are often considered. These are of the form; (F(t)=\int _{x_{0}(t)}^{x_{1}(t)}f(x;t)\,dx)

In this formula, t is the argument of the function F, and on the right-hand side the parameter on which the integral depends. When evaluating the integral, t is held constant, and so it is considered to be a parameter. If we are interested in the value of F for different values of t, we then consider t to be a variable. The quantity x is a dummy variable or variable of integration (confusingly, also sometimes called a parameter of integration).

Wolfram (Mathematica) views the definition of Parameter as:

The term “parameter” is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when plotting, performing mathematical operations, etc., are termed “variables,” while those that are not explicitly varied in situations of interest are termed “parameters.” For example, in the standard equation of an ellipse


x and y are generally considered variables and a and b are considered parameters. The decision on which arguments to consider variables and which to consider parameters may be historical or may be based on the application under consideration. However, the nature of a mathematical function may change depending on which choice is made.

And so the term Parametric Design is based on the various parameters that define the curving nature of these designs as lines or forms.

Parametricism and Parametric Architecture-What’s the Difference?

As with many other fields, there are often differing definitions of a similar topic, and so is the case for this topic as well. Parametric Architecture also has another title, which is called Parametricism.

In a segment on the history of Parametricism, it’s stated that it, “emerged as a theory-driven avant-garde design movement in the early 1990s, with its earliest practitioners – Greg Lynn, Jesse Reiser, Lars Spuybroek, Kas Oosterhuis among many others – harnessing and adapting the then new digital animation software and other advanced computational processes that had been introduced within architecture much earlier by pioneers like John Frazer and Paul Coates, but that only spread to make an impact within avant-garde architecture in the last 10–15 years.” [8]

Patrik Schumacher, of the Zaha Hadid design group, has said that he, “believes the work of Frei Otto (1925 – 2015) is a precursor of Parametricism, as Frei “used physical processes as simulations and design engines to ‘find’ form rather than to draw conventional or invented forms.”” [8]

He uses this term in reference to “parameterization ” as defined as:

“Parametricism is a style within contemporary avant-garde architecture, promoted as a successor to post-modern architecture and modern architecture. The term was coined in 2008 by Patrik Schumacher, an architectural partner of Zaha Hadid (1950-2016). Parametricism has its origin in parametric design, which is based on the constraints in a parametric equation. Parametricism relies on programs, algorithms, and computers to manipulate equations for design purposes.” [4]

This definition coincides with the topic of the “Parametric equation”, which is defined as:

“In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object.” [5]

If you’re familiar with calculus you may recognize that many of these equations are based on the process of determining the curving form of lines, and the areas underneath these curves. Using these forms of mathematics, these curves can be created in 3D software systems such as CATIA, Rhino/Grasshopper, Nemetshek and some of the newer versions of AutoDesk/AutoCAD offerings.

According to Schumacher, “parametricism is an autopoiesis, or a self-referential system, in which all the elements are interlinked and an outside influence that changes in one alters all the others.” [6]

This type of “nodal interconnection” of objects, shapes and forms in a parametric format creates structures and architecture that has more flowing forms, that juxtapose the more common box-like, rectangular buildings of the 20th century and earlier.

So these Parametric Designs in many ways can be defined as “curving architecture” or “curvilinear architecture”. This is in juxtaposition of much of the common architecture from the past, from the rectangular shapes of the Parthenon to the rectilinear designs of most homes and skyscrapers.

What Do Curving Shapes and Mathematical Forms have to do with Health and Wellness?

If you asked a child in the modern world to draw a house, it is likely that they will draw a square or rectangular box with a triangle roof (half a square), a rectangle as a door and a square window or two. This along with a rectangular shaped chimney and perhaps a long linear fence that is in the basic shape of a rectangle, this would probably be very similar to the reality of how they view the symbol of a house.

And this viewpoint as a “symbol” of a house can actually be quite profound, in terms of the viewpoint of how a building is viewed in a child’s or adult’s psyche. If these objects of archietcture are seen as symbols based on squares and rectangles, how does that impact their view on nature and the world they live in?

This may not seem like a big deal, until you take the time to realize that very little in nature is actually shaped this way. Your own body is mostly curves and are not square and not rectangular in any form. Most of the natural world is curvilinear, whether it be as the human and animal form, or the shapes and designs of landscapes. Most of the world is curving, even your internal structure as a skeleton has a natural curving format. Your skull, spine and rib cage is based on curves and while many of your bones are somewhat linear, they do have a slightly curving shape to them. They also have a curving design as individual bones, with a larger portion of the bone at the ends and thinner interiors, which creates a curving shape and is not just a straight line.

This is particularly important in terms of the human connection to the natural world. Without a sense of connection to the natural world and to oneself, how can humans feel connected to nature? And if you can’t feel connected to the natural world, can’t it be challenging to see the importance of conserving and taking care of, and living with, nature?

This topic is a main focus of Biophilia, and more details on this topic can be read here.

This, perhaps, is a challenge for the modern-day human, as a key for survival for many centuries has been to strive to protect oneself against nature and the potential harms of natural issues, from weather and the elements, to the various creatures and organisms that could cause harm.

By creating shelter to remove humans from these natural harmful scenarios, the buildings of the past were more about survival than they were about thriving.

Yet as humans have become more technologically advanced and capable, our architecture has allowed for shelter to become more separated from the natural elements. And this can be seen in the International Style of architecture, where these buildings appear similar in form and function no matter where they are in the world. Since the early 20th century, the International Style could provide shelter from any weather conditions – from a hot, dry desert to cold, snowy climate. Whether it be the rainy tropics or the dry tundra, these buildings could provide separation from nature and the natural surroundings, and provide the required climatized shelter for human survival.

However, this is also a current day issue in how modern day architecture, cities, and humanity in general have developed. The striving for survival in any environmental setting has also removed ourselves from the natural world, and segmented us with the illusion that we are no longer connected. In order to find survival through shelter, humans have created buildings that have given the appearance that we do not need to be concerned about the natural world. In fact, the focus of shelter in the past was to specifically separate ourselves from the world in order to ensure our survival.

And it is this mentality of overcoming nature that has removed our mindset as being connected to nature. And this is a major issue in the current day and age for several reasons.

The first and perhaps most obvious is that we as humans ARE nature. Our bodies are composed of natural elements, from the average 70 percent content of the human body being water, to the many natural elements that our bodies use to grow our skin, bones, and organs. Elements such as carbon and silica provide the components that we depend upon for life, and are the same carbon and silica that much of the natural world is composed of.

While our bodies are literally a part of nature, we also depend on the health of nature for life itself. The water we drink, the food we eat, and the quality of the environment determines the quality of our own health. If we pollute, destroy or destruct the very nature that supports our lives for surviving, then that which we destroy will end up destroying humanity as well.

So What Does this have to Do with Parametric Design?

You may be wondering what all of this has to do with parametric design. And this is a good question.

If we view parametric design as just a curving forms, then we are missing the big picture view of the psychology of this topic. This viewpoint is, in my opinion, a short-sided view of parametric design. And what is missing is the potential for a connection to nature as well as our own bodies and our own health.

And the part that we are missing on this subject is that these curving shapes and designs remind us of our natural origins and our connection to nature. The psychology of being around and living within rectangular shapes and forms, and nothing but grided streets and developments, brings us further away from remembering that we are not only living in nature, we are nature.

By having more curvilinear shapes and parametric forms in our everyday built environments, we are reminded both consciously and subconsciously of our connection to the natural world. And as neuroscience is also showing, these curving shapes and forms can allow humans to be less stressful and to be less in fear and fight or flight mode. This, in turn, allows a more cognitive capability to recognize and value our natural surroundings that provide us with life.

When we have these natural forms reminding us of nature’s inherent forms, it can also provide a connection for us to the natural world. And the more that we can feel connected to the natural world and to our own bodies, the more we can find the importance and empathy for preserving and conserving nature.

The importance of Curving Designs in the Future

Parametric design may be one of the most important design approaches in the future of architecture for a few reasons.

First is the biomimetic philosophy that can be combined with this approach.

These curving designs also support a number of developing fields whose findings show knowledge and wisdom as a result of studying natural designs, and applying this knowledge can form the wisdom of future architecture.

A good example of this is the fields of biomimicry and biophilia, where each of these fields is studying the benefits of nature, yet in two different formats.

Biomimicry studies the designs, shapes, and functionality of nature. By understanding how nature has solved a particular design issue, humans can then study this solution to find the core processes of these designs. This information can then be implemented to achieve a similar design issue that humans are striving to solve.

An example of this is the approach of Santiago Calatrava, whose designs are often based on biomorphic shapes. These designs are not necessarily meant to emulate or reconstruct an exact duplicate of the shapes, yet to understand why an organism may be shaped in a way and to use this knowledge as applied wisdom to solve a design issue.

In Eugene Tsui’s book Evolutionary Architecture, Dr. Tsui uses the anthropomorphic and biomorphic forms in a design process based on the wisdom of these design shapes and forms. By analyzing these natural designs, this design knowledge can be used to utilize fewer materials, yet also provide better structural integrity – for instance, while preparing the structure to handle earthquakes. His house design in San Francisco, “sometimes called “Ojo del Sol” (“Eye of the Sun”), is also known as the “Fish House” and, according to Tsui, is based on the anatomy of a tardigrade. The materials used in making the Ojo del Sol include inexpensive and recycled materials that draw inspiration from the Cholla cactus, which is virtually fireproof. Tsui designed the house with the goal of making it the “safest house in the world,” intended to survive fires, earthquakes, flooding, and termites. [1]

If you view both of these designers’ approaches, you will see that their striving to create beautiful forms, with the superior engineering of nature, can provide both a function and form that supports a more advanced approach to architecture.

Biophilia, or the Biophilia hypothesis, is defined as the “idea that humans possess an innate tendency to seek connections with nature and other forms of life.” The term biophilia was used by German-born American psychoanalyst Erich Fromm in The Anatomy of Human Destructiveness (1973), which described biophilia as “the passionate love of life and of all that is alive.” The term was later used by American biologist Edward O. Wilson in his work Biophilia (1984), which proposed that the “tendency of humans to focus on and to affiliate with nature and other life-forms has, in part, a genetic basis.” [2]

To combine these design aesthetics with engineering brilliance is also to embrace biomimicry with biophilia to design architecture that can best support human and biological health and wellness.

Parametric Architecture and Human Wellness

And this brings us to the part of the conversation that involves human health. These parametric designs also have a great potential for human wellness. By creating shapes of buildings that are curving, it can allow a more relaxing scenario for human physiology. According to new developments and findings in neuroscience, by not having sharp, angular forms, the amygdala and brain center (responsible for stress and fear triggers), are not as triggered, and this can prevent fear and provide less stress.

By decreasing emotional, psychological, and physiological stress, along with providing less toxic building materials, these designs can also support better overall health and wellness.

So these curving designs are not just soothing to the emotions, they have a direct positive impact on the human experience and can support a sense of well being.

The Architecture of Life

There is another facet of parametric architecture that is perhaps less data-driven in arriving at concrete evidence, and more of a silent yet real connection to nature that we as living beings can benefit from.

In the writing “The Architecture of Life“, Donald Ingber discusses the design of living organisms in terms of, “A universal set of building rules…to guide the design of organic structures–from simple carbon compounds to complex cells and tissues”. In this writing, Dr. Ingber talks about both the material design of nature, yet also the architectural designs of all living organisms.

And if you look at these design ideas relative to the work of Buckminster Fuller and Frei Otto, you can also see a common thread connecting the natural design of the world with human-designed buildings. Both were proponents of tensile structures and designs that could be seen as anthropomorphic, and as you view their work you can see this thread of commonality. From the tensile structures of domes to the curving arches and open area spans that their spaces created, their designs drew from the natural world and reinterpreted this knowledge into their own designs.

As stated in a previous paragraph, according to Schumacher, “parametricism is an autopoiesis, or a self-referential system, in which all the elements are interlinked and an outside influence that changes one alters all the others.”

And this description of parametricism is exactly the same as the “nodal interconnectivity” that Dr. Ingber describes as the architecture of cells and tissues.

And it is this thread of commonality that I believe has an inherent connection to that which we see and what we are as humans. By viewing designs of structures and architecture that mimic our own architecture of our bodies, while also showing the similarities between the architecture of your cells and that of nature, inherently connects us to the natural world.

While we don’t fully understand how the mechanics of entrainment really works, we do know that objects often synchronize when they are placed in the same environment. An article in Science Direct defines Entrainment as, “a process that leads to temporal coordination of two actors’ behavior, in particular, synchronization, even in the absence of a direct mechanical coupling.” [3]

An example of this is when you put any clock in a room full of clocks, they eventually will all synchronize to the same rhythm. “Entrainment is perhaps the most widely studied social motor coordination process (Schmidt, Fitzpatrick, Caron, & Mergeche, in press). For instance, two people in rocking chairs involuntarily synchronize their rocking frequencies (Richardson, Marsh, Isenhower, Goodman, & Schmidt, 2007), and audiences in theaters tend to clap in unison (Neda, Ravasz, Brechte, Vicsek, & Barabasi, 2000).” [4]

So what if entrainment is also impacting us on an architectural level as well? For instance, if we are spending most of the time in rectangle, box-like shapes and forms and looking at these large rectangular designs such as city-scapes, can that attune us to shapes and forms that are less natural, and perhaps remove us from our connection to nature?

If most of the natural world has more curving shapes and forms, from the flowing designs of streams, rivers, and countrysides to the curving shapes of plants and animals, can the curvilinear forms of the built environment help to attune us back to nature, and bring us to a future that is in more connection and reverence with nature and the natural world?

The definition of health is,

health (n.)

Old English hælþ “wholeness, a being whole, sound or well,” from Proto-Germanic *hailitho, from PIE *kailo- “whole, uninjured, of good omen” (source also of Old English hal “hale, whole;” Old Norse heill “healthy;”

Therefore, the meaning of being unhealthy is to not be whole or to be disconnected and fragmented in some way. And so, part of the process of health and well-being is to have this sense of wholeness regained, especially for people in places that are fragmented. To include the re-connection back to nature and the natural world is a facet of this curving architecture that can support this process.


While the International Design Style was created at a time when survival was key, now that humanity has been able to find this survival, the next step would be to strive for thriving, and this would include the return to wholeness and health. And perhaps using these parametric, curvilinear shapes and forms in our everyday architecture and built environment designs, can help us to reconnect to nature via entrainment and in so doing can reconnect us with our own good health.

These concepts, connected with fields such as organic architecture, biomorphic design, biomimicry, biophilia and many others, strive to not only emulate the surroundings in a natural format, yet to understand the design core in function and form, and then create human-based designs in architecture that both support life and promote health.

This design approach, combined with the fields of environmental psychology and evidence-based design, further enhances the integration process to achieve the goals of health and wellness.

Perhaps much of these concepts are new to the general public at this time, and while there are still many unknowns at this time in history as to what the outcome and result over time will be, the process of integrating these multi-faceted topics and concepts into a cohesive whole can certainly provide a better connection between humans and the natural world. And this development of healthier built environments can support a reconnection to nature and a world that can be enjoyed.

The combination of these parametric designs to help to reduce the material needs of construction, while providing better engineered structures is one major benefit. This, combined with the decrease in stress levels that curving forms can support, can provide a deeper connection where architecture is providing a form of “Medicine” to those who live around and within such architecture. These shapes and forms can provide less stress and a more relaxed environment on a physiological level.

And this should provide a hopefulness of the future that in today’s day and age is not easy to find. These newer designs can bring humanity back to nature while providing forward momentum into a more positive and healthier future.