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.

fractal-nature

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).

escher-koch

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)

snowflakesbyme.jpg

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.

snowflake

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.

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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).

corpusmuseum-denmarkobservatory

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.

dancinghouseandothers

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:

franklloydwright

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.

tajmahal

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.

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.

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 at an Early Age

Two articles look specifically at the role of geometry in school, from primary through to university level, and discuss the difficulties with trying to create a universally valid curriculum.

In The Place of Experimental Tasks in Geometry Teaching: Learning From the Textbook Designs of the Early 20th Century, Taro Fujita and Keith Jones write:

“A characteristic feature of geometry is its dual nature, in that it is both a theoretical domain and perhaps the most concrete, reality-linked part of mathematics.”

It is this duality that creates difficulties for teachers who are faced with trying to bridge the gap between theory and practice within the classroom, two parallel studies that many children struggle to fathom at the same time (Fujita, Jones, 2004). It is interesting that the two threads are difficult to weave together in a mathematical setting when theory and practice so often converge in nature and in art and design.

In The Role of Intuition in Geometry Education: Learning From the Teaching Practice in the Early 20th Century, Fujita Taro, Keith Jones and Shinya Yamamoto question the role that geometry has in a teaching curriculum and suggest that a slight reshuffle of the specification of geometry might be in order, specifically focusing on intuitive geometry–where children show an ability to “see” geometrical shapes and manipulate them in the mind to solve problems (Fujita, Jones, Yamamoto, 2004). Interestingly, their article highlights an address given by J. Perry, Professor of Engineering at the Royal College of Science, in 1901, who questioned the value of teaching Euclidian geometry to children (Fujita, Jones, Yamamoto. 2004). Perry was an advocate for experimentation and a more intuitive approach to geometry. This is fascinating to me as a creative; the idea that mathematics can be approached in a more creative way, by being encouraged to simply observe our surroundings. This method would likely appeal to children who do not think analytically or struggle in a scientific or mathematical setting. It also opens the floor to a wider selection of children being brought into geometry study and develops the ability to think outside the box or push expectations.

This is another aspect of my own graphic design that I want to develop further: rather than simply designing how I think I should design (trying to anticipate the expectations of others), I’d like to grow my own ability to “see” design in new ways, try new approaches and not concern myself with only doing what is popular in the moment. Seeing a subject as far removed from art and design as geometry in a new and creative way encourages me to push my own boundaries and methods.

Back to geometry. This intuitive ability to see shapes and use them to solve problems ties in with the paper Modularity and Development: The Case of Spatial Reorientation by Linda Hermer and Elizabeth Spelke. Hermer and Spelke explore children who, during development, share some similarities with animals in how they spatially place themselves in their surroundings using geometric cues. Their study revealed that the developing brain is more in tune with room geometry than with lesser-defined patterns or other defining factors (like odour, colour, etc). At an early age, we reorient ourselves in accord with the shape of our surroundings (Hermer, Spelke. 1996), meaning that geometry is playing a large part in our natural development, before it is formally introduced or taught. That we are subconsciously aware of geometry relative to ourselves is an exciting concept and something that could be explored in advertising–particularly advertising aimed at children.

Attempts at tying geometry with a more creative, intuitive practice have been made in a number of key learning equipment. Not all of the following toys were intended for children but have been adopted over the years as useful developmental tools.

The Spirograph, whose origins date back to the mid 19th Century, was originally created to help prevent bank note forgery, but it eventually became a popular 2D geometry drawing game. Spirographs involve the creation of hypotrochoid (a circle rolling inside a fixed circle) and epitrochoid (a circle rolling around the outer edge of a fixed circle) roulettes. A similar method known as Guilloché is still used on paper currencies, passports and security seals today, which means we have all come into contact with spirograph patterns.

The Lego Group was founded in Denmark in 1932 by Ole Kirk Kristiansen and, since then, Lego has become one of the most popular toys of all time. Providing children and adults alike with Automatic Binding Bricks of different shapes and colours, it teaches us to think not just creatively but also geometrically and in 3D. Lego is an effective puzzle-solving tool which exposes us to science, technology and engineering. For example, constructing a complex object like a bridge takes thought, development and trial and error. These small plastic geometric shapes teach children to patiently think through problems to reach a desired outcome. Through playing with different coloured Lego bricks, children can also learn about symmetry, colour combinations and patterns, and really let their imaginations run wild.

The Helix Oxford Maths Set was launched in 1935 by Helix and offered its famous geometry set. It wasn’t until 1959 that they began to mould their own plastic tools, which are the tools I used when growing up. The set includes a ruler, set squares, protractor, compass and pencil, pencil sharpener and eraser.

Finally, the paper Fortune Teller was first introduced in the book Fun with Paper Folding (Murray and Rigney; 1928) and is a more informal geometric toy that many will recognise from their school days.

fortuneteller01

The fortune teller was originally called the “salt cellar” and was intended to stand on a table while the four pockets contained condiments. Fortune Tellers were a popular game at school and I remember creating them with my friends (usually asking most pressing questions such as “Which member of Take That will I marry?”).

References

Fujita, T; Jones, K (2004): The Place of Experimental Tasks in Geometry Teaching: Learning From the Textbook Designs of the Early 20th Century. International Congress on Mathematical Education (ICME-10). Copenhagen, Denmark.

Fujita, T; Jones, K, Yamamoto, S (2004): The Role of Intuition in Geometry Education: Learning From the Teaching Practice in the Early 20th Century. 10th International Congress on Mathematical Education (ICME-10). Copenhagen, Denmark; 4–11 July 2004.

Hermer, L; Spelke, E (1996): Modularity and Development: The Case of Spatial Reorientation. Elsevier – Cognition 61. Department of Psychology, Cornell University, Uris Hall, Ithaca NY.

Murray, William D., Rigney, Francis J (1928): Fun with Paper Folding. Fleming H. Revell Company.

Spirograph | Denys Fisher | Science Museum

Guilloché Patterns | Ed Pegg Jr., February 9, 2004

Lego

Helix Oxford Maths Set

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:

geometric-pattern-large

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:

beehivegeometry

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:

Geometric-Design-01

I had come up with a list of possible connotations alreadymystical, 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