Understanding and Soap Bubbles
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
"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
- Films can only meet three at a time and
they do so symmetrically, so that the angles between them are 120
- 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).
- 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
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
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
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