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Love, Understanding and Soap Bubbles

Simon Thomas

Pioneer of that now termed the Art/Science forum, Simon, who lives and works near Fowey, is highly regarded as an artist researching the underlying patterns of nature through observation and scientific study. In this essay he describes the background to the sculpture 'Moment of Truth', based on the structure of soap bubbles.


I have come to consider mathematics not only as a language to describe the weave of life, but also as the thread of its fabric.

For someone who learned more on the riverbank than in the classroom my connection with mathematics has evolved along less orthodox lines than some.  My first brush with mathematical magic was at primary school, when with a compass I drew my first "flower".


"Orb" by Simon Thomas

Many years later whilst a post-graduate student at the Royal College of Art I rediscovered geometry's flowery gateway, and this time armed with compass, pencil, and ruler, embarked on a journey into the wonderland of divided space.  In the early days I employed my new found knowledge and skills to create practical devices such as templates and the like, but soon enough I was seduced by the process itself, investigating the properties of various proportions, sequences, and symmetries.


"Planeliner" by Simon Thomas

Humanity's sense of beauty has long been a topic of debate, thought of by some as purely subjective, whilst others prefer the "reflection of God notion".  It is my belief that there is a strong relationship between natural efficiencies and our perception of what we call beautiful.  Why are we predisposed to appreciate beauty in such things as the design and fabric of eg a dragonfly's wing? Could it be that it is fascinating because throughout human evolution we have learned to recognize "efficiencies" as a vital part of our survival mechanism; an appreciation of how to gain most through least possible effort?


"Eye" by Simon Thomas

"Small Worlds" by Simon Thomas

Studies of soap-bubbles

Throughout my study of soap bubble foam geometry I have been transported by a sense of wonder in the beauty of this optimized fluid structure. It is an example of a dynamic system where the parameters of geometric possibilities and the laws of physics co-exist in an ephemeral harmony.


Closed and open celled foams seem to be found across the scale range of existence, in organic and inorganic structures.  From quantum foam at Planck length, right through to that state suggested in the research of cosmologist Margaret Geller, where the distribution of galaxies within the cosmos appear to be located within a foam structure.

Soap bubble foam is a randomly arranged congregation of air pockets varying in volume, encapsulated by films of detergent/water.  Detergent lowers the amount of surface tension experienced by the water it is mixed with.  If air is forced through the soapy water it will surface as a bubble.  When this process is repeated many times, these bubbles find themselves positioned within a colony of neighboring bubbles, and through this coming together, the original sphere bubbles transmute into polyhedral cells. 

Within the apparent chaos of closed cell foam there are certain constants.  Plateau's laws tell us about the shapes and connections of soap films:

  1. Films can only meet three at a time and they do so symmetrically, so that the angles between them are 120 degrees.
  2. The lines along which they meet are themselves joined in vertices at which only four lines (or six films) can meet.  Again they are symmetric, so that the angle between the lines is 109 degrees (the tetrahedral, or Maraldi, angle).
  3. The films and the lines are curved in general: the average amount by which the films are bowed in or out is determined by the difference in pressure between the gas on either side (Laplace's law).



I am in the process of creating an artwork which aspires to reflect the geometric conditions of this water matrix, and aims to celebrate the mesmeric relationship between beauty and natural efficiencies. 

The most fruitful experiments I've conducted to date have been achieved with the help of a particular molecular modelling node.  The node is that associated with the fourfold carbon bonds found in diamond, the one where the four equally spaced valency pegs would fit into the four corners of a regular tetrahedron.  The angle between pegs is approximately 109 degrees and is known as the "Maraldi".  This is the same symmetry we find at the very heart of the four edged corners of foam.


Figure 1. Carbon atom nodes
with "Maraldi" angles

Figure 2. Polyhedra indicating
relative edge curvatures

The nodes, in combination with flexible bond rods of various lengths, create a network where the rods are obliged to deform through curvature, seemingly just as the edges of foam cells do.  The positions and alignments of the nodes, and the way rods set in certain arrangements correspond to certain curvatures, is striking in its resemblance of the cell edges and corners of real foam.

Larger individual cells can have convexed, concaved, flat and saddle shaped faces, all part of the same cell.  This indicates a rule that wherever a cell is larger in volume than a neighbour, the face it shares will always be concaved into the larger one.

The relationship between cell size/pressure, and its geometric expression, is very much influenced by the Maraldi angle sat in the cell corners.  The smaller cells of higher pressure create the most convexed curvature.  Development of this modelling system with its 109 degree angle, and through observations of real foam, have informed me that the maximum convexed curvature in rods (or edges) is witnessed when they form part of triangular faces as found on tetrahedra.  A little less convexed edge curvature is found as part of a square face, approximately no edge curvature with pentagonal faces, and edges gradually increase in negative curvature (concaved) for faces with more than five edges. 

Of note here is that an edge is not exclusive to one face, or "ring" of edges.  With each edge sharing three faces, and the faces having an angle of 120 degrees set between them, it is likely that the curvature of one edge is the mean of these three sets of force.


Figure 3. Clustered "Rings of edges" showing
positive, neutral, and negative curvature

The artwork

Foam structure is an eminent expression of energy conservation, and in my opinion beautiful because of this. 

Now, for me the science of the subject is only half of the story, I also have to evolve an artwork, which above all has presence and meaning. 

I have worked through quite a few ideas concerning the look and build-technique of such a sculpture, and within the particular circumstances of my current commission I have decided to more or less stick with uncomplicated look of the modelling system, a design I feel is both technically plausible, and visually arresting.  One thing I have done in order to fortify the visual impact of the piece is to exponentially increase the cell sizes in the vertical direction, adding a sense of the foam "billowing forth".


Figure 4. Modelled foam complex in frame

Figure 5. "Cell" being cast

In this way the artwork will describe the edges and corners only, of a foam complex.  Fabricated in 6mm stainless steel rod, every weld will be carved/ground back to form an "oily" minimal surface look.  The feel will be one of a continuous homogeneous surface over the whole network, not lots of spars "spot welded" at their ends.

In order to transfer accurate co-ordinate information from the plastic model to the sculpture itself I have taken a cast from every one of the 71 "cells".  These are composed of a heat resistant plaster based material (developed on the job) and will be used to weld upon. The rods will be rolled to the correct curvatures before being incorporated into the final design.  Finally, the frame within which the plastic model has been located will be utilised to offer datum points, ensuring a faithful representation of the forces freely expressed by the tensile plastic model.


Figure 6. Seventy one "cells/ formers", the edges
of which are to be used for welding upon


This is an abridged version of the full essay available at simonthomas-sculpture.com