Geometry in Spiritual Art and Design

Geometry is not only associated with mathematics, art and nature. One application that I have wanted to explore in depth since choosing my keyword is geometry as it occurs in spiritual art and design, a concept I encountered first hand while travelling in Southern India in the year 2000.

I was lucky enough to arrive in India at the start of the Pongal Festival, a Tamil harvest festival in which people celebrate the sun and appreciate the gods and goddesses for a successful harvest. This festival takes place every year in January. Generally the women in a household rise each morning and draw intricate geometric patterns on the ground outside their houses or on the floors within the houses. These patterns are created from various materials: rice flour, chalk powder, rock powder or synthetically coloured powders.

The Tamil people of Southern India believe that by drawing the kolams and paying homage to the harvest, the goddess Mariyamman will grant them blessings and increase the prosperity of their home and family (Laine, 2009). At the time of seeing these patterns—of walking among and across them with my bare feet—I had no idea that they would leave a lasting impact on my creativity in years to come. As a young woman, I was not so keenly aware that this practice is only carried out by women and that it is a way for them to invite well-being, express their spirituality, but also measure their creativity and dexterity (Ascher, 2002). The tradition of kolam creates a space for Indian women to experiment art and also science. It is the meld of religion, spirituality, creativity, mental discipline and mathematics. Kolam drawing connects women with the wider community (the harvest) and with the family (the blessing), but it is also a personal and internal exercise.

This is an interesting practice that relates to my work on the MA because most of the kolams are represented using geometric shapes and formations. The repeating, symmetrical patterns range from basic white kolams to elaborate, kaleidoscopic designs.

Kolam is a form of visual language, and interestingly computer scientists have become interested in the algorithmic nature of some of the designs as a way of creating picture languages (Ascher, 2002). This only reinforces the idea that many of the patterns, passed down from mother to daughter and spanning countless generations, are a highly skilled practice and require a taught technique.

My experience with kolam and later with mandala has led me to create my own concentric geometric designs, paying homage to the things that are important to me. The following design was created in 2017 using mandala as inspiration. This is one of a four-part series work in progress based on the seasons.

A mandala (Sanskrit for “circle”) is another form of concentric geometric pattern drawing that is conducted across the world in different countries. Specifically healing mandalas are created by cultures including Tibetan Buddhists and Navajo people in North America. In his article Mandala Constructing Peace Through Art, Tom Anderson discusses the drawing and deconstruction of mandalas as a way to explore the idea of “reconstructing” —a caring, cooperative and self-reflexive community project (Anderson, 2002). They are intended to protect or repair either people or the environment. Their aim is to restore balance and harmony—a theme that plays a large role in other areas of my research into geometry. These processes also bring a social harmony and reinforce shared beliefs, morals and values (Anderson, 2002). In its own way, it is a form of art therapy and is seen as a positive practice.

This relates to art in general as a form of visual messaging, a shared experience but an experience that is at the same time deeply personal to whoever is viewing the art.

In Sacred Geometry, Deciphering the Code, author Stephen Skinner writes that geometry is the archetypal patterning of many things, perhaps all things (Skinner, 2006), and this notion has become more and more evident to me as I have read, researched and written about geometric shapes in their many forms and applications. Over the months my sense of geometry being universal has grown stronger: it is a form of common language between humans, a way of reasoning in the sciences, a way of communicating within our belief systems, and a way for us to figure out where we are in relation to the rest of the world.

Skinner goes on to discuss geometry dating back to ancient times, most likely beginning in Egypt, with temples and other sacred spaces designed around geometric formations and scientists using geometry to map the movement of the heavenly bodies and the seasons (Skinner, 2006). These geometric buildings were intended for people to use to communicate more directly with their deities. The harmony and precision of the structures made them sacred. I believe this ties in with a common thread I have encountered throughout my research, which is that people take comfort and solace in the structured, organised, harmonious nature of geometric shapes.

With this knowledge and my own personal interest in pattern-making and mandala / kolam design, I am eager to explore geometric design more in my work. It is a strong language and an effective way of communicating ideas and messages across the world, something that language cannot alone achieve. In this regard, art transcends other forms of communication and touches people from all countries and all walks of life.

References

Anderson, Tom (2002): Mandala Constructing Peace Through Art. Art Education Journal, 55:3, 33-39.

Ascher, Marcia (2002): The Kolam Tradition. Sigma Xi, vol. 90, No. 1. The Scientific Research Honor Society. North Carolina, USA.

Laine, Anna (2009): In Conversation with the Kolam Practice: Auspiciousness and Artistic Experiences Among Women in Tamil Nadu, South India. University of Gothenburg, School of Global Studies. Sweden.

Skinner, S (2006): Sacred Geometry, Deciphering the Code. Sterling Publishing, New York, London.

Artist Spotlight – Manolo Gamboa Naon

Manolo Gamboa Naon is a Creative Coder from Argentina. He creates interactive installations, video games, data visualisation, websites and tools for digital advertising. He describes himself as “obsessed with generativity” and likes programming images in which he works with geometric patterns, textures and overloading.

I found Manolo’s work a few months ago while browsing Behance, and was immediately drawn in to his designs. They spark with colour, shapes and motion, and there is often an incredible sense of depth in his work thanks to his relentless layering techniques.

For me his work stands out because it seems like every geometric shape has been placed carefully and thoughtfully to reach the overall outcome. It must be a painstaking and time consuming process putting some of these works together, and Manolo does it prolifically—indicating that he simply loves creating these deeply complex compositions.

In his essay Nature of Abstract Art, Meyer Schapiro writes that in stripping away the literal subject and the bias of the artist, we are left with pure aesthetic elements, shapes and colours.

“The new styles accustomed painters to the vision of colors and shapes as disengaged from objects and created an immense confraternity of works of art, cutting across the barriers of time and place.”

This way of thinking meant that all art was suddenly valid, from children’s paintings to the scribbles of people with mental disorders, and all deserved of consideration (Schapiro, 1937). Art is subjective, as are most creative fields, and perhaps more so when it comes to abstract, where shapes and colours exist as their own entities and remain open to interpretation.

To me, Manolo’s work feels almost stream-of-consciousness that produces beautiful complicated works. They are not uniform patterns and there is not often perfect symmetry, but the use of geometric shapes gives off an illusion of order and precision. This is an interesting balance to me: abstraction and order. I love how Manolo achieves this and makes it look effortless.

A number of his pieces are reminiscent of colourful fantasy cityscapes. One in particular I am drawn back to time and time again is this piece posted in July 2018:

My interpretation is that I am looking down onto many circular buildings, the faint grey lines and intersections signifying the many pathways and possible directions people can travel, with the larger circular shapes housing their own networks and pathways within. It could also represent a person’s brain, with its innumerable neural pathways and connections, the colours representing the different areas of the brain working for different purposes. Manolo is a creative coder who also makes video games, which is possibly why when I look at this piece I see a landscape full of areas to traverse and explore.

While I enjoy most of Manolo’s pieces, there are one or two that do not work so well for me. For example:

This piece is far more minimal than his other work and in its own right fine, but when viewed in his gallery sitting next to his other pieces it almost looks like a mistake. While I appreciate the simplicity of many geometric shapes and their different meanings this piece does not speak to me or tell me a story. Within the context of his other pieces I feel this one does not fit. Many of Manolo’s other creations feel like well-rounded stories or places for great exploration. Unfortunately he rarely adds a commentary along with his art so I am not sure what this represents to him or where the idea came from.

References

Schapiro, Meyer (1937): Nature of Abstract Art. Published in Marxist Art Quarterly, from the American Marxist Association.

Visit Manolo’s website | Manolo on Behance

Naturally Occurring Geometry

One fascinating resource I encountered in my research is the book The Fractal Geometry of Nature, by Benoit B. Mandelbrot. It has been important to me to write about naturally occurring geometry as it crops up in a lot of my reading and is something I am inspired by in my own work.

Nature is fragmented and multi-faceted. This is where Mandelbrot got the idea for the term fractal, from the Latin frangere, meaning “to break” (Mandelbrot, 1982). But the fragmentation of nature means that there are an infinite amount of possible geometric shapes and formulas, surpassing Euclidian theories that there is a finite number of geometric shapes available to us. In art and design, Mandelbrot suggests that we are more likely to accept abstract art that resembles fractals because it is subconsciously familiar to us.

M. C. Escher, whose famous tessellations were inspired by the Islamic tiles that he saw while on a trip to the Alhambra in Spain (Van Dusen, Scannell and Taylor. 2012), is often described as a fractal artist with a keen interest in the properties of patterns found in the natural world. His pattern Circle Limit III repeats at various sizes and scales without losing its geometric formation (Fig. 1) and is reminiscent of naturally occurring geometry in plants and flowers. Similarly, the Koch Snowflake, a fractal curve that was presented by Helge von Koch in 1904, is a scalable geometric pattern that can repeat indefinitely (Fig. 2).

Mandelbrot’s vision of geometry was unrestrained by the mathematical theory that preceded him, although this is not to say he does not respect those theories that came before; rather, he builds upon them and tries to bring them into better harmony. He believed that mathematicians shied away from the possibilities that nature presented, and attempts to meld science with philosophy. This blending of precision and boundless creativity is a pairing that mirrors the job of a designer working in the present day.

“One must also recognize that any attempt to illustrate geometry involves a basic fallacy. For example, a straight line is unbound and infinitely thin and smooth, while any illustration is unavoidably of finite length, of positive thickness, and rough edged. Nevertheless, a rough evocative drawing of a line is felt by many to be useful, and by some to be necessary, to develop intuition and help in the search for proof. And a rough drawing is a more adequate geometric model of a thread than the mathematical line itself.” (Mandelbrot, B. 1982. P22)

Here Mandelbrot expresses the difficulty in representing something as broad and infinite as a geometric line, but appreciates that we must find ways to root our understanding of geometry—in the form of drawings and art—and pay homage to the shapes present around us. As an artist and designer, this is interesting to consider: shapes are merely representations of things we might otherwise consider unfathomable. We are trying to make visual sense of something as vast and infinite as the universe.

Mandelbrot also points out that while many believe that mathematics, music, art and architecture seem to be related to one another, it is only a superficial connection, as—in the case of architecture—one building can follow strict Euclidian geometry, but another building can be more rich in fractal aspects (Mandelbrot, 1982). I see the similarities drawn between geometry and art, mathematics and music often, most recently when studying Swiss Style graphic designer Josef Müller-Brockmann’s poster for Beethoven’s symphony, where the geometric choices are believed to have represented the structure of the symphony. In my Practice 1 assignment I look at modern geometric Swiss Style art used to portray grunge band posters from the 1980s-1990s, although I struggle to draw the connections and similarities between something that is rigidly structured, ordered and precise with something that stood for distortion, being true to yourself and individuality.

Mandelbrot also writes: “It is widely held that minimal art is restricted to limited combinations of standard shapes: lines, circles, spirals, and the like. But such need not be the case. The fractals used in scientific models are also very simple (because science puts a premium on simplicity). And I agree that many may be viewed as a new form of minimal geometric art.” (Mandelbrot, B. 1982)

These snowflakes are from a winter-themed graphic design project I worked on last year for a local restaurant and shop. At the time I was not thinking in terms of geometry, but I was faced with the problem of deciding on the shapes and formations of the snowflakes, as there were so many possibilities. Even before I began reading about geometry I was aware of the challenge of representing natural complexity in art.

In Fractal Architecture: Organic Design Philosophy in Theory and Practice, James Harris explores the fractal geometry of nature as the inspiration for some forms of architecture where the natural “recursive mathematical derivation” of form creates a new structure that is removed from the more logical and rigid Euclidian geometry (Harris, J. 2012). Harris believes that philosophers and mathematicians created geometric theories to cope with the unfathomable randomness of the universe, which was beyond their comprehension (Harris, J. 2012). I believe this is a natural human behaviour—the need to make sense of the vastness of the universe and all the endless possibilities within. We search for and even yearn for our own kind of structure within the study of complex, naturally occurring structures.

In the paper Is the Geometry of Nature Fractal? written for Science Magazine, David Avnir, Ofer Biham, Daniel Lidar and Ofer Malcai offer an alternative idea:

“Fractals are beautiful mathematical contructs [sic] characterized by a never-ending cascade of similar structural details that are revealed upon magnification on all scales. Over the past two decades, the notion has been intensively put forward that fractal geometry describes well the irregular face of nature.” (Avnir, O. et. al. 1998)

While it is difficult to believe that all geometry in nature holds a perfect symmetry and fractal behaviour, I do not think that theorists like Mandelbrot were trying to constrain nature within the definition “fractal”, but rather offer another view of something that cannot easily be understood or contained. Again, a way for us to wrap our minds around this deeply complex and mysterious world surrounding us.

As part of my Practice 1 assignment, I am looking at the multi-faceted nature of geometry and how low-poly art emulates the geometric shapes found in crystals and ice—neither of which are uniform in size and shape, and yet both of which form a structure with many faces that reveal different colours and reflections. Mandelbrot raises the question in the opening of his book “Why is geometry often described as cold and dry?” and I would like to explore geometry used to expose a depth and intricacy behind the “cold, dry” surface.

References

Avnir, David; Biham, Ofer; Lidar, Daniel; Malcai, Ofer (1998): Is the Geometry of Nature Fractal? Science, Jan 2nd – Vol. 279, Issue 5347, pp. 39-40.

Harris, James (2012): Fractal Architecture: Organic Design Philosophy in Theory and Practice. University of New Mexico Press.

Mandelbrot, Benoit B. (1982): The Fractal Geometry of Nature. W.H. Freeman and Company, New York.

Van Dusen, B; Scannell, B. C; Taylor, R. P: A Fractal Comparison of M.C. Escher’s and H. von Koch’s Tessellations. Published in Fractals Research, School of Education, University of Colorado, Boulder, Colorado, USA.

The Scutoid Has Landed

Just a short post about something that happened recently which relates to my chosen keyword geometric. A paper written by Pedro Gómez-Gálvez and Pablo Vicente-Munuera was published in Nature Communications in July 2018 introducing a new geometric shape that is linked to the metamorphosis of tissue cells during organ development. This shape is called a Scutoid*.

“As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the architecture and packing of curved epithelia remains largely unknown. Here we show by means of mathematical modelling that cells in bent epithelia can undergo intercalations along the apico-basal axis. This phenomenon forces cells to have different neighbours in their basal and apical surfaces. As a consequence, epithelial cells adopt a novel shape that we term “scutoid”.” (Gómez-Gálvez, P. et. al. 2018)

Nature has found a way to conserve energy and pack cells more efficiently, and we are only now uncovering this phenomenon. While the science of the scutoid falls outside of my main stream of research, I do find it fascinating that yet again geometry plays a major role in nature as much as it does in mathematics. It is this blending of science and the creativity of nature that arises time and time again. The more I read about geometry the more I feel that it links everything–from art and design to the fabric of living creatures and the universe itself.

Gómez-Gálvez and Vicente-Munuera also write:

“In addition to this fundamental aspect of morphogenesis, the ability to engineer tissues and organs in future critically relies on the ability to understand, and then control, the 3D organization of cells.” (Gómez-Gálvez, P. et. al. 2018)

Discovering this deeper level of our biology will no doubt have an impact on how effectively and efficiently we approach medical and scientific problems in the future. The new shape could also play a role in art and design. 

References

Pedro Gómez-Gálvez, Pablo Vicente-Munuera, Antonio Tagua, Cristina Forja, Ana M. Castro, Marta Letrán, Andrea Valencia-Expósito, Clara Grima, Marina Bermúdez-Gallardo, Óscar Serrano-Pérez-Higueras, Florencia Cavodeassi, Sol Sotillos, María D. Martín-Bermudo, Alberto Márquez, Javier Buceta, Luis M. Escudero (2018): Scutoids are a geometrical solution to three-dimensional packing of epithelia. (www.nature.com/articles/s41467-018-05376-1) Nature Communications, 2018.

* According to Science Daily (28th July 2018), the new shape was labelled “Scutoid” because of its resemblance to the scutellum, the posterior part of an insect thorax or midsection. (http://www.sciencedaily.com/releases/2018/07/180728084136.htm)

Architectural Geometry

“In an architectural context, geometry is often used as an ordering device, that is, a way to link spaces to functions.” (Williams, K; Ostwald, M.J. 2017)

In the introduction to vol.19 of the Nexus Network Journal, Manifestations of Geometry in Architecture, Kim Williams and Michael J. Ostwald highlight that the geometry of architecture is not only a functional measure to ensure the most efficient and structurally sound building, but also to create a more appealing aesthetic.

“Once a structure is codified and built, geometry can add beauty to a design.” (Williams, K; Ostwald, M.J. 2017)

This idea rings true to me as a creative who has explored geometric graphic design for a long time without paying mind to the precise mathematical foundations that fortify such design. I rarely associate mathematics with beauty, not as much as with its creative cousins art and music, but in the precise geometry of buildings there can be found a great sense of rhythm, movement and intent.

Architectural design can range from the simple to the complex, just like with any other creative field. Examples of creative architecture include the Corpus Museum in the Netherlands which advertises itself as a “journey through the human body,” and the Spiraling Treetop Walkway in Denmark, created to give tourists a bird’s-eye view of the forest without disturbing the natural surroundings. Both embrace nature in their own unique way, and both attempt to represent the purpose (subject) of the building (Fig. 1).

Geometric architecture also encompasses the bizarre. For example, the Dancing House in Prague (Fig. 2, left). Designed by Frank Gehry and Vlad Milunič, this unusual building that leaps over the intersection symbolises the direction the Czechoslovak people have taken to move away from the totalitarian rigidity of the past.

The other two photos (Fig. 2, right) are buildings that do not conform to conventional architecture but rather deviate to create a new and unexpected environment and an entirely different experience. I thought about how this relates to contemporary design and my own work. I feel that we are often prone to working within pre-defined boundaries and expectations, but sometimes it is necessary to not just step outside the box but take a positive leap. The above architects were not afraid to break tradition; to them, it was extremely important to do so.

Architect Frank Lloyd Wright designed impressive buildings that worked alongside their surroundings rather than dominated them. Lloyd Wright himself described his buildings as “organic architecture” (Pfeiffer, B. 2004) and you can find examples of this in his work:

In Geometry And Architecture, Steven Firth writes:

“The uses of geometry in architecture tend to be instrumental, dovetailing with the process of building as a species of order. The modulation and arrangement of plans and the surfaces of elevations go hand in hand with this fiction, but also depend upon geometrical play.”

The implication here is that geometry exists to bring order and structure to a landscape or a people, but I cannot help but feel when looking at Lloyd Wright’s harmonious meshing of man-made and nature that there is a synergy, with the one blending seamlessly with the other. The water flows beneath the house and out over the rocks, much in the same way that people flow around and through the house, and in the way the creative ideas flow through the architect or designer.

The notion that geometry can influence a person’s perception of a building cropped up frequently in my reading. In Aesthetics of Simulated Soiling Patterns on Architecture, Carlota M. Grossi and Peter Brimblecombe explore the reactions in people to different soiling found on buildings, in an attempt to see if there was a preferred type of pattern. The idea is that if there is a less obnoxious soiling of architecture then building managers wouldn’t have to have their buildings cleaned so often. To me this is a study with only a tenuous connection to my own research, but what I found interesting was the results: people generally prefered a more uniform type of soiling–a pattern that they could make sense of–rather than a randomised formation.

The more I dig into geometry and shapes, the more it seems that we are drawn to pattern, repetition and order.

Finally, I looked at geometry at work in architecture from cultures other than my own. One fascinating article written by Carol Bier is Art and Mithāl: Reading Geometry as Visual Commentary. Bier explores the idea that the decoration on Islamic monuments is often viewed through a Western lens (Bier, C. 2008), but the pervasive use of pattern must be an expression of something more than simple ornamentation. The implication is that elaborate decoration somehow implies a lack of deeper meaning and significance. Bier also writes:

“It now appears that aperiodic patterns with five-fold symmetry related to that of quasicrystals may have been understood by craftsmen in Iran, if not mathematicians, hundreds of years before this phenomenon was discovered in the West.”

It might be naive of us to assume that geometric pattern relates to decoration or mathematics.

In the year 2000 I spent three months in India, and had the opportunity to see the Taj Mahal up close. The mausoleum itself is comprised of countless geometric shapes and precise lines and symmetry, but inset into the white marble are row upon row of black onyx script. The two details combined created an incredible sense of peace, flow, history and reverence.

Again, it fascinates me how geometry can be used in architecture to evoke different feelings from those viewing it. I do wonder how an opinion might shift if the story of a building is changed: if you transformed the Taj Mahal, built as an elaborate mausoleum by emperor Shah Jahan for one of his wives, into the stately home of a wealthy oil family, built to show off status and power. Suddenly the romantic spirit of the building is changed. The geometric components remain the same, the patterns are no less intricate and the work that went into it was no less laborious, but now it becomes a structure of arrogance and vanity.

This relates to my Practice 1 project, where I want to look at how small changes made to a geometric design can change people’s opinions and perceptions. My project relates to branding and logo development, but from my research into architectural geometry I can take away that geometry does not always have to be rigidly ordered to work; it can be combined with more fluid design (elements surrounding it) and they can work together harmoniously.

References

Bier, Carol (2008): Art and Mithāl: Reading Geometry as Visual Commentary. From Iranian Studies, Vol. 41, No. 4, Sciences, Crafts, and the Production of Knowledge: Iran and Eastern Islamic Lands.

Firth, Stephen (2010): Geometry and Architecture. Architectural Theory Review, Taylor & Francis Online.

Grossi, C. M.; Brimblecombe, P. (2004): Aesthetics of Simulated Soiling Patterns on Architecture. School of Environmental Sciences, University of East Anglia, Norwich.

Pfeiffer, Bruce Brooks (2004): Frank Lloyd Wright, 1867-1959: Building for Democracy. Taschen, Germany.

Williams, Kim; Ostwald, Michael J. (2017): Manifestations of Geometry in Architecture. The Nexus Network Journal, Architecture and Mathematics, vol. 19. Birkhäuser Publishers, Switzerland.

The Geometry of Textiles

In her symposium paper Textiles and the Body: The Geometry of Clothing, Madelyn Shaw talks about the mathematical principles of weaving material used in clothing:

“Interlaced threads create square or triangular grids, techniques such as knitting or crocheting can make grids of any shape, from triangular to polyhedral. Those who make clothing transform flat fabric planes into three-dimensional forms through a variety of means.”

Patterns occur not only on the finished fabric as a visual design—they are integral to the structure of the garment itself. A single thread can generate complex geometric patterns that most people wearing the finished garment will never see with the naked eye or look for in the first place. In the Textile Research Journal article Hierarchy of Textile Structures and Architecture of Fabric Geometric Models (Lomov, S.V; Huysmans, G; Verpoest, I; 2001), it is posed that the hierarchical structure of fibrous materials influence the mechanical behaviour of textiles. A well-developed weave can result in sturdier fabric and a longer lifespan of the garment. Additional fabrics can also be added to make the inherent geometry of the weave varied and more complex, although this raises the possibility of structural inconsistency.

There are a number of recognisable garments that utilise geometric shapes: the kaftan, the poncho, or the Pakistani jumlo (Shaw, M. 2006), and a number of high fashion designs draw on geometry to enhance and bring attention to different areas of the body (Fig.1).

An interesting point to note about the inherent geometry within textiles are the changes that take place throughout the course of a garment’s lifespan, from the moment it is woven to the moment it is discarded. Force and pull can lead to stretching at various stages and none of the shapes that are created during the sewing will remain in a solid state—they will constantly fluctuate with wear and even become permanently distorted in some cases of intense wear. The force applied to yarns and fibres creates a deeper and ever-changing level of geometry. In the paper Mechanics of Textile Composites: Micro-Geometry (Miao, Y; Zhou, E; Wang, Y; Cheeseman B. 2007) this is referred to as “micro-geometry.”

I decided to look more closely at how pressure and force can change the nature of geometry within textiles. I spread one of my cardigans across a table and then took a photo of the fabric in its unworn, untouched state. Fig.2 shows the change in the geometry of the weave when the jumper was pulled at either side.

A more obvious type of geometry that can be applied to a garment is the visual design and pattern, often created by using different colours or different materials. Repetitive pattern brings structure, gives flow and rhythm, and can be appealing visually and aesthetically (Perkins, M. 2015). During my research I wanted to know why we are drawn to geometric patterns and what it is about patterns that we find pleasing. Mathematician Ian Stewart says that we live in a universe of patterns (Stewart, I. 1998), from naturally occurring patterns in the makeup of plants, the formation of clouds in the sky, in topography, to genealogical patterns and the structure of our families. The patterns that surround us every day provide our lives with symmetry, repetition, order, movement and rhythm (Kraft, K. 2015), and it is hard to believe that patterns do not emotionally and intellectually influence us all in some way.

Perhaps this is why we are drawn to structure and order; is necessary in society, and for many people it is necessary in day to day planning and living. Geometry, being present in many aspects of our lives, even down to the clothes we wear, could play more of a role in how we feel and what we think than we realise. 

In Design Aesthetics: Principles of Pleasure in Design, Paul Hekkert discusses the meaning of aesthetics, and argues that works of art are mostly produced for the purpose of gratifying the senses (Hekkert, P. 2006).  This could go doubly for textiles, whose tactile and visual experience combines to produce a stronger reaction. But is there a deeper logic at work in the things we are drawn to? Hekkert also raises the question of why we like certain objects—what is it about a pattern or the feel of a product that reaches us on a deeper level than the purely visual? Something well-structured could subliminally tell us that it is sturdy and safe. A geometric pattern can also imply stability and structure, and bring comfort in its repetition and order. Hekkert writes:

“As demonstrated, adaptations have evolved to serve functions beneficial to our survival. It would have been helpful for the development of these adaptations if things in the world around us that contribute to these functions were reinforced (Tooby & Cosmides, 2001). In other words, it must be beneficial for humans to seek cues or patterns that serve these adaptive functions. We therefore (have come to) derive (aesthetic) pleasure from patterns or features that are advantageous to these functions.”

If this is the case, then we instinctively look for recognisable or pleasing patterns as a way of choosing the safest, most beneficial course of action. It would be an interesting experiment to see if somebody wearing a geometric pattern and somebody wearing a randomised pattern influences how trustworthy or approachable others perceive them.

Through my research into geometry used in textiles I have discovered that there are a number of different ways geometric shapes can play a part in our garments and the fabrics surrounding us. Geometry is worth considering when creating a textile and pattern is important for a designer working with textiles. Additionally, geometry and pattern can be used to evoke different meanings and responses and also influence the integrity of a textile.

As a result of my research I am keen to develop patterns that I can use in my own work and share as resources for other designers. In the past I have created patterns for clients (one was printed on a wedding shirt, which relates to the topic of this post) but I would like to approach pattern design with more clarity and focus, using the knowledge I have picked up from reading about patterns in textiles.

References

Hekkert, P (2006): Design Aesthetics: Principles of Pleasure in Design. Delft University of Technology, Netherlands.

Kraft, Kerstin (2015): Textile Patterns and their Epistemological Functions. Textile: The Journal of Cloth and Culture.

Lomov, S.V; Huysmans, G; Verpoest, I (2001). Hierarchy of Textile Structures and Architecture of Fabric Geometric Models. Leiden University, Netherlands.

Miao, Yuyang; Zhou, Eric; Wang, Youqi; Cheeseman, Bryan A. (2007): Mechanics of Textile Composites: Micro-Geometry. Department of Mechanical and Nuclear Engineering, Kansas State University, USA.

Perkins, M. (2015): Print & Pattern : Geometric. 1st edition, Laurence King Publishing, London.

Shaw, Madelyn (2006): Textiles and the Body: The Geometry of Clothing. Textile Society of America Symposium Proceedings, University of Nebraska – Lincoln.

Geometry in Origami

Many of us are exposed to origami at some stage in our early years, either at school or through the media we consume. It can be used as a tool for learning, as an aid for focusing, a way of embracing our creative side, or simply for relaxation and pleasure. In this post I explore origami and its various uses.

In the paper A Note on Intrinsic Geometry of Origami, Koryo Miura, Professor and Director of the Research Division of Space Transportation, says: 

“The mathematical expression of an origami process is a transformation of a flat piece of paper into a polyhedral surface which expresses something.”

The word origami means “fold” and “paper” in Japanese, and can range from basic shapes to extremely intricate folded designs and formations. While Koryo Miura’s paper focuses on the mathematical aspects of origami, this sentence jumped out at me immediately as a creative practitioner, and I can relate it to my own creative processes and results.

I have always imagined origami to be a personal venture and it is often referred to as an art rather than simply a hobby. This could be because it provides both mental and physical challenge and problem-solving, introduces you to geometry, symmetry and spatial thinking, and deals with shapes and clean lines. It instills the ability to follow instructions and listen carefully, but it can also bring a deep sense of satisfaction and catharsis if followed through, and it helps cultivate creative thinking. The element of trial-and-error teaches patience and persistence (if folded wrong, a piece can become difficult or even impossible to continue). It is a timeless practise, accessible to anyone with access to a sheet of paper, and holds appeal to both children and adults alike.

In the article Analysis of Design Application on Structural Model of Origami, by Hsun-Yi Tseng, it is believed that: 

“Origami started out as a traditional art form found in religious rituals and folk customs before evolving into a creative art for leisure and recreation.”

My own attempt at origami. I went for something fairly simple: a trinket box design I found a few years ago. It has been a while since I’ve folded this box and it took a degree of fiddling, studying the tutorial, and testing my own dexterity before I could finish it. While there are areas that need improvement (corners not quite closing), I am overall happy with the result and it was worth the time invested. This type of origami also has its practical uses – the box will hold paper clips, pins and other small pieces of stationary on my desk.

Returning to my earlier statement that I can relate expression through origami to my own creative processes, I found that folding this box focused my attention immediately. This is something that happens frequently when I begin a new design, whether its a practical or digital piece, particularly if there are intricate elements to it. Many designs rely of different parts coming together to create meaning and resolution.

The box was not without some frustration, with some of the flaps awkward to slot together, but once the triangular shape started to come through these frustrations lessened. Perhaps this is because I could see the box taking shape. 

In the book The Use of the Creative Therapies with Sexual Abuse Survivors, editor Stephanie L. Brooke writes:

“Another important therapeutic aspect of Origami is physical and psychological effect of the act of folding paper, which allows us to use the left and right spheres of our brains at the same time (Shumakor, 2000).”

Much like zen drawing and art therapy, origami can become a form of catharsis with its repetitive motion and tendency to focus attention. I frequently engage in ASMR (Autonomous Sensory Meridian Response) exercises as it relaxes my mind and body, and one of my main triggers is the folding, cutting, touching and manipulation of paper and card. Paired with the joy of solving a puzzle, creating a complex or beautiful design, and focusing attention, I can see why origami is used in art therapy and mindfulness practises to enhance a sense of wellbeing or help process a traumatic experience.

One of my favourite origamists is Ekaterina Lukasheva, whose manages to merge incredibly complex and precise modular designs with a great sense of movement and an organic feel:

I can’t help but think that she was inspired by naturally occurring geometry in the world around her, a topic I will blog about in a separate post.

Tomoko Fuse’s modular origami boxes are also worth noting, combining basic geometric design with gentle motion and peacefulness. The structure of the box itself creates the pattern, with no need for additional decoration or intricacies:

The Sonobe Cube Lamp is another lovely and practical piece of origami, based on the Sonobe module (believed to have originated from Mitsunobu Sonobe and Toshie Takahama), and illuminated by Judith at Origami Tutorials:

Also the beautiful Hydrangea Tessellation, originally created by Shuzo Fujimoto:

References

Brooke, Stephanie L. (2006): The Use of the Creative Therapies with Sexual Abuse Survivors. Charles C. Thomas Publisher; 1st edition.

Miura, Koryo (1989): A Note on Intrinsic Geometry of Origami. First presented at the First International Meeting of Origami Science and Technology, Ferrara, Italy.

Tseng, Hsun-Yi (2017): Analysis of Design Application on Structural Model of Origami. Published in 2017 International Conference on Applied System Innovation (ICASI).

Learn how to fold the origami triangular box here. See more of Ekaterina Lukasheva’s origami here. Tomoko Fuse Modular Box here. Origami Tutorials.

Discover ASMR. There are some incredible ASMR artists out there and they are easy to find on YouTube, but the ones I am always drawn back to are Charlotte Angel and Rhianna at ASMR Magic.

Keyword Study #1: Geometry

For the second week of our Masters we were asked to pick one word from our personal statements and create a keyword study. I chose the word geometry. It doesn’t sound like the type of keyword you would expect on an art course, does it? But geometric shapes and patterns are all around us – in nature, in our homes, in architecture and our surrounding environments, in the media, in our brands, and in our creative consciousness.

I am fascinated by geometry used in spiritual art and design and how the formation of shapes and construction of patterns can give us a sense of faith, hope and surety. It can also provide a sense of structure in our belief systems and a way to visually interpret the security that our beliefs bring us. This is something I have encountered while travelling and I plan to create a blog post focused solely on my experiences with spiritual geometric art in the future.

Geometric shapes are also popular in logo and brand creation. Could this be because they also provide a sense of security and structure in the brands that we encounter day to day? Are we more likely to trust a brand whose logo utilises geometry than one that favours a more fluid and relaxed approach?

I also wonder if geometric designs can be deconstructed or reformed to create a more jagged and unnerving feeling, perhaps signifying the breakdown of stability? This is another element to my keyword that I plan to experiment with over the next few weeks.

For week two, we were also given the task of finding:

1. A literal example of our keyword
2. An abstract example of our keyword
3. Another artist’s interpretation of our keyword

For my literal image I went with a basic geometric pattern:

This pattern was originally created for a brush-making company for use on toothbrush packaging. The pattern features the company brand colours and was designed to be eye catching but still retain a corporate feel. The angles and lines were intended to create a sense of structure and maturity, and the fact that I did not use a repeating pattern implies that the company strive for innovation and thinking outside the box. I tried a version with a repeating pattern and though tidy it did not give off an impression of the company or the product development process. One thing I don’t think worked was the intricacy of the overall design; it’s extremely busy, and teeters too close to the edge of playful which does not fit with the brand. If tasked to create further toothbrush artwork I doubt I will use such an intricate geometric pattern. If the shapes were bigger and more clearly defined, the implication that the company is sturdy and secure might come across more clearly. I did research on other well-known toothbrush brands and noticed they often followed a common theme, with a prevalence of curves and swooping shapes, and I wanted this packaging to stand out from the crowd.

My first abstract image shows a naturally occurring geometry:

For my second abstract example, I decided to conduct my own experiment and created a geometric shape in Illustrator (this took approximately ten minutes). During a conference with my fellow students I asked people to tell me what the following image evoked in them:

I had come up with a list of possible connotations already: mystical, mathematical, spiritual, abstract, fantasy, ritual. There were also a couple of ideas that I hadn’t considered, including circuitry and constellation (and zodiac). After the conference I continued to look at the design and draw connections. I ended up with two more ideas: hoax in the context of crop circles, and insignia in the context of an organisation or gang.

It’s interesting that the connection to a series of basic shapes depends on a person’s interests, beliefs and ideas they have absorbed elsewhere.

Finally, my third entry is a piece by artist Manolo Gamboa Naon, which you can see on Behance here. I can stare at Manolo’s art for ages and get drawn deeper and deeper. It feels almost like I’m looking down onto a strange and colourful cityscape. The faint grey lines and intersections are like many pathways and possible directions people can travel, with the larger circular shapes like buildings with their own networks and pathways within. It could also represent a person’s brain, with its innumerable neural pathways and connections, the colours signifying the different areas of the brain working for different purposes. Manolo is a creative coder who also makes video games, which is possibly why when I look at this piece I see a landscape full of areas to traverse and explore.

References
Beehive Photo | Manolo Gamboa Naon