14. Patterns in Nature (part three)

Time to talk again about patterns in nature and the connections to landscape design.  In earlier posts I wrote about the Golden Ratio, and branching patterns.  I’d like to get into good ‘ole geometry this time, so let’s start back in something like 6th grade and think about circles, squares and triangles and see where that takes us…

Simple Geometric Building Blocks

Way back at the beginnings of modern science, people like Pythagoras saw basic geometric forms as the building blocks of everything in nature.  He found circles, squares, triangles, pentagons and hexagons in all kinds of natural forms and saw their recurrence as evidence of inherent harmony and regularity.   Although it can be tough to find them in their literal, symmetrical forms, these shapes do seem to underlie all kinds of natural phenomenon.  For example, there are hexagonal forms in things as varied as bee hives, snowflakes, and rock formations such as the basalt rock columns of Devils Postpile near Mammoth, California.

The 3-D version of the five basic shapes are the Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron, together called the Platonic Solids.  These are the only 5 possible Regular Polyhedrons, those that have faces with the same shape and size.  Since those were more mystical times, these shapes were a big part of what is now called Sacred Geometry, a sort of mystical / philosophical idea that these pure forms underlie all the forms in nature and are evidence of a conscious, intentional creator behind it all.  I won’t even attempt to prove or disprove this concept, my point is that these simple shapes have been seen as something of great significance for quite a while.  In fact, the concept of all matter being made up of these shapes isn’t all that far from the modern scientific conception of atoms and molecules.

Both the 2-D shapes and the Platonic Solids were given many symbolic meanings, for example being associated with the 5 elements:  tetrahedron = fire, cube = earth, icosahedron = water, octahedron = air, dodecahedron = the void/ether.  Because of their commonality in nature and their symbolic meanings they are found in human-designed structures throughout history.  If a person is so inclined today, these geometries can again serve as inspiration for giving some symbolic meaning to a design.

The Vesica Piscis

A simple example is that of the vesica piscis, which is the overlapping of two equal circles so that the outer edge of one touches the center of the other.  The shape formed in the middle resembles a sort of lens or eye shape that has been connected to many different abstractions.  For example, it can be seen to resemble the overlapping of the sun and moon in an eclipse, with the middle piece symbolizing a gateway between the opposing worlds.  Connecting the intersection points yields an equilateral triangle, and a hexagon can be drawn by connecting the intersections of the triangle, as you see in the diagrams above.  Before the time of computer drafting, people were able to generate these forms with simple drawing tools and use them as a basis for all kinds of architectural elements. I used is as the basis for a theme camp design as you can see below.

Tile Patterns

You can take this method of connecting intersection points further and further and generate some really interesting patterns that you will recognize in ceramic tile shapes, mosaic patterns, weavings and other pieces of art and architecture from many time periods and cultures.  By simply inscribing circles within squares (called the “squaring of the circle”) and connecting intersection points you can derive all kinds of patterns that can be used in paving designs, such as those shown below.  Religious architecture around the world works off these kinds of basic geometries and the connecting of points, using them as symbolism for their beliefs.  For example the gothic window frame is formed by the edges of 3 circles overlapping in a triangular arrangement to symbolize the 3 aspects of the Trinity.

The Geometric Depths

In some of the books I read, they really start to go deep on this idea and draw connections between certain numbers, shapes, and proportions that start to get a little too mystical for my scientific upbringing.  However, I do find it remarkable how many different cultures and societies have utilized basic geometric shapes to symbolize deep concepts and philosophies.  I definitely see value in bringing some of that into a design as a fun way to put a little more meaning into the shapes, colors, and patterns used.  Some related approaches to design based on patterns thought to be inherent in nature are Feng Shui and Vastu Shastra, but that’s a whole other topic that will have to wait.

At a more practical level, these geometries can form the basis for all kinds of patterns in the landscape, from patio tiles to fencing and trellis structures.  These sorts of patterns may not seem to connect us to nature quite as directly as branchings or Fibonacci proportions, but in a sense they represent the basic properties of the space that nature grows within.

References:

Patterns in Nature, by Peter S. Stevens

Sacred Geometery, by Miranda Lundy

Sacred Geometry – Philosophy and Practice, by Robert Lawlor