Geometry, color, meaning

2D digital art

3 | mandala

geometry

Contents

*William Blake, The Ancient of Days, 1794*

GEOmater

Now, aqua in buccat. I’ll make you to see figuratleavely the whome of your eternal geomater. And if you flung her headdress on her from under her highlows you’d wheeze whyse Salmonson set his seel on a hexen-gown.
James Joyce, Finnegan’s Wake, p. 296

Geometry is a very specific way of creating order, and vector graphics is a very specific way of working with geometry. But there is more than meets the eye — literally — when we discover the many uses of geometry to create an image. Marco Frascari, an Italian architect and design theorist, proposes specific ways geometry can be used in image-making.

Channeling Irish author James Joyce, who was famous (or infamous) for mashing up words to create new meanings, Frascari appropriates Joyce’s pun word GEOmater. Frascari reveals how Joyce combined the words matrix, mater, and meter with geology and geometry into an allegory describing the influence of design upon destiny.

Three geometries

Frascari observes three co-existing functions for, and names three inter-related kinds of, geometry:

prediction: Mantic geometry
creation: Structural geometry
observation: Body geometry

MANTIC GEOMETRY

Mantic is a term associated with prophecy and divination. We see it as a root for words such as romantic (as in visionary).

Mantic geometry projects a possible future, making thinkable the yet-to-be-imagined, associated with layout and format.

An example will be your use of a layout device, such as the rule-of-thirds grid, for composition:

Rule-of-thirds mantic grid
in a vertical format

STRUCTURAL GEOMETRY

Structure is an organization of interrelated elements in an object or a system.

Structural geometry controls pattern and hierarchy, making invisible relationships visible, associated with creation through ratio and proportion.

An example will be your use of polygon construction in developing a mandala drawing structure:

Top: hexagon construction
Bottom: square construction

BODY GEOMETRY

In physics, a body is a discrete unit of material that is movable in 3-dimensional space. A body is also one’s physical self.

Body geometry determines tangible volumes, spaces, and surfaces, making material immaterial, through the application of geometric primitives: polygons, polyhedra, cones, cylinders, and spheres.

An example will be how you develop shapes and color into meaningful visual elements:

Creating the illusion of space and transparency through color

In the image of color applied to the geometric construction above, we might see an interesting illusion. Look closely: does it feel like you can see layers of overlapping planes anywhere? Gyorgy Kepes describes this phenomenon:

If one sees two or more figures overlapping one another, and each of them claims for itself the common overlapped part, then one is confronted with a contradiction of spatial dimensions. To resolve this contradiction one must assume the presence of a new optical quality. The figures are endowed with transparency… . Transparency however implies more than an optical characteristic, it implies a broader spatial order. Transparency means a simultaneous perception of different spatial locations. Space not only recedes but fluctuates in a continuous activity. The position of the transparent figures has equivocal meaning as one sees each figure now as the closer now as the further one….
Gyorgy Kepes, Language of Vision

Our upcoming exercises in color theory will introduce the idea that hue, saturation, and brightness relationships among colors can create ambiguous spatial relationships among planes. Examples by three artists from the Bauhaus — Wassily Kandinsky, Paul Klee, and Josef Albers — provide compelling visual proof of Kepes’ discussion of phenomenal transparency’s power to create multiple spatial readings.

Each artist provides a text that reveals much about their views of the relationship between color and geometry: Kandinsky, Point and Line to Plane… Klee, the Pedagogical Sketchbook… Albers, Interaction of Color. Note the examples of work by each artist. How does phenomenological transparency, generated through color plane relationships, lead to spatial ambiguities?

These are phenomena we will exploit in our project by learning how to control and use color

*Wassily Kandinsky, Composition VIII, 1928*

*Josef Albers, Homage to the Square, 1965*

Creating meaning

There is no such thing as good painting about nothing.
— from a letter by Mark Rothko and Adolph Gottlieb to the Art Editor of the New York Times

This project explores relationships between symbol and representation, metaphor and metonym, and devices of geometry, color, and imagination, to be drawn in layers in Illustrator. Our selected representation will be a mandala, which we build by structuring it with Frascari’s GEOmater, and expressing it using the transparency relationships borne of geometry and color.

But what will the mandala be about?

Metaphor and metonym: figures of speech

To answer that question, we’ll work with a common strategy in art: to create a figure of speech, but not of a verbal kind. This one will be applied in a visual context. One kind of figure of speech, a metaphor, relates similarities among things that are otherwise different: He was a deer in the headlights doesn’t mean someone magically turned into a deer. Rather, it means he and deer share the quality of being surprised by something. Another kind, a metonym, relates things through association: Philadelphia won the Super Bowl doesn’t mean millions of citizens were on the field of play. Philadelphia associates with the unspoken presence of the Eagles football team, which won the game. Go Iggles!

OK. So what will we base our figure of speech on?

Earth Air Fire Water

Ou mandal will incorporate a visual metaphor or metonym generated from one or more of the four Classical elements: Earth, Air, Fire,Water. These pre-modern elements are a universal human theme, a part of our collective unconscious, and do not in and of themselves carry meaning. It is the artist’s interpretation of our larger human condition that charges a work with resonance that speaks to other people. Individual interpretation can create rich figures of speech or shallow clichés.

Whether by figuration or abstraction, by art or design, we can see a broad range of individual sensibility applied to the theme of the classical elements, starting with the fascinating anthropomorphic portraits by Giuseppe Arcimboldo. He predates Surrealism by centuries.

*Giuseppe Arcimboldo, Water, ca. 1566-70*

The Elements across centuries and cultures

The Greek philosopher Aristotle articulates a firm model of the physical world made up of earth, air, fire, and water in his treatise, Physics, written in 350 B.C.E. Expressions of the classical elements are not limited to Ancient Greece, however. The following span across cultures East and West—Greek, Indian, Chinese—and across time—from the 5th century B.C.E. to the 21st century C.E.

*The Four Elements of Aristotle, based on a diagram from Isidore of Seville, Liber de responsione mundi, 1472*

*Chinese Wu Xing,* *a diagram of elements or phases* *used in feng shui and elsewhere*

*Agni, God of Fire, Hindu bas relief c. 1000 C.E., Cleveland Museum of Art*

*Jan Brueghel the Elder and Hendrick van Balen, Abundance and The Four Elements, ca. 1615*

*D. Stolcius von Stolcenberg, Viridarium chymicum, 1624, a diagram of elements in 16th century alchemy*

Contemporary expressions of the Elements

Although the literal idea of all matter being comprised of earth, air, fire, and water has long been discredited by science, contemporary takes on the theme as a more symbolic reality abound.