Friday, January 31, 2014.

San Antonio, Texas

Third Minimal Surface Blog Entry

(Conclusion of our Physical Model)

Sketch of our model, done in Rhino 5.0 for Windows.

Sketch of our model, done in Rhino 5.0 for Windows.

Changes on Our Minimal Surface Model:  The diagonal shaped columns.

As mentioned on previous notes, Frei Otto’s comprehensive investigation on minimal surface structures sort of opened our minds and made us discover how versatile and strong these tensile and minimal structures could be.

Looking at pictures of old precedents for minimal structures particularly the one from the Denver circus in 1917:  We began to notice something quite interesting.  Some of the masts supporting the tent were not vertical but  diagonal.

A Denver Circus Tent from 1914

A Denver Circus Tent from 1914

This gives us another opportunity to change our design by incorporating diagonal columns.

A minimal structure is a building still made from minimal materials, which can be assembled quickly, efficiently, economically and safely – but now we can add diagonal columns that along with the tension and compression – it will give our model a different form.

This shape or form is still derived from the modeling techniques of the soap film experiments.

Soap film is a minimal surface, and retains its shape with the addition of diagonal columns.   All of the forces that are exerted on it are still in equilibrium.    This gives us a more abstract optimal shape.

Mr. Mclellan also offered some suggestions on our model, which we adopted quickly.

He showed us on some of Frei Otto pictures how the membranes were cut or transformed to geometric figures that meet at one central point, or node.

He also stimulated our imagination with the concept of murmuration, and the mathematical concept of continuous differentiation.

Murmuration is a flock of starling birds flying together creating a series of geometric patterns.  Their movement is synchronous, rapid, and fluid.

Murmuration of birds

Murmuration of birds

Graph of a murmuration of birds

Graph of a murmuration of birds

Mr. Mclellan expressed that essentially the birds may be turning to the left or to the right, south or north, but for the human eye they seem to do it uniformly and together as in a squadron of air force airplanes.

Anyhow, murmuration of starlings with its distinctively geometrical shapes provides a great point of inspiration for us in search of a more organic shape for our model.

Continuous differentiation, also helps us with form finding for is a term used in Calculus which generally means if we have a function (y = F (x)), the result will change when we change the input value.   This result can be graphed with a curve, a straight line, or a line of different heights or different depths.

In other words, Calculus can also stimulate our imagination in the search for another set of forms for our project.   Sort of like the Rhino Grasshopper software produces forms and shapes mathematically.

graph of a function

graph of a function


It is light, safe, economical and can be assembled or dismantled easily.    It will provide the volume shape we need for our project at the McNay museum.

Our minimal structure would  be respectful to nature and will not require a slab, or major alterations on the lot, making it possible to leave trees and landscaping intact.  The appearance of our model would still look organic and nature-like, resembling a mountain, a valley, a jellyfish, like a cell under a microscope, or like a flock of birds.

Our Old Type vs. Our New Type

Last week, we experimented with a simple tent that simulated some of Frei Otto’s experiment.  In fact, it looked like a hup tent.

hup tent

hup tent

This week’s Minimum Surface construction has the following shapes:

  1. 4 point tent
  2. Double curve
  3. Parabolic
  4. Hyperbolic
  5. Single curve
Hyperbolic Roof.  Rhino drawing.

Hyperbolic Roof. Rhino drawing.

Materials  (A revised list)

This week’s structure was made of:

  1. Copper mesh
  2. Soap bubble skin
  3. Copper masts
  4. Soldering wire

We also tried to make some models out of coffee stirrers joined by twist ties from a produce store.  However, we did not photograph it and quickly abandoned it because it did not have the clean form we desired.

The Evolution of Minimum Surface construction through the Ages

The Tents or membrane structures of yesterday gave us the concept of using diagonal masts or columns.

We can clearly see this on the tepee picture below:



With today’s technology and new plastic materials and steel masts (now positioned diagonally), we are  ready to defy high winds and possible earthquakes.

Definitions  (Recapitulation)

Soap film continues to be Iconoclastic and so are the minimum surface structures.  (Nerdinger, pages 18-22).


The shapes of the minimal structures we mostly experimented were:

  1. Hyperbolic,
  2. Parabolic,
  3.  Square,
  4. Transformed or Bent Square.

Objective (Revised)

Our objective is still to design a minimal transitional structure, which would connect the old Mc Nay to its new wing, providing a path, shelter, and a place to transition from one building to another.   Something that could define the departure from the old, representational form of art displays to the new and more modern displays of art.   But, now with the bent or diagonal columns – our form will change significantly resembling the geometric way a flock of birds fly together, or like a school of fish on a lake or at sea.

We will maintain the connection with nature through its gardens because the structure will have a clear roof not affecting the vegetation under the roof or beside it – we may be able to let the trees grow through it.

We reduced our shapes to the following geometric shapes:

  1. Hyperbolic,
  2. Circle,
  3.  Parabolic,
  4. Square,
  5. Transformed Square


 A Minimum structure can be built using tension and compression, tensile material or fabric, and anchor support.    Except that now we added the bent or diagonal columns.  We did simulate our model by increasing our scale to an object that is 4 feet long and about one foot wide.   Now, we have to start working on a digital model and figure out how would it look at a larger scale.

Model Materials (a new revised list)

This week we changed our recipe.   We added less soap and skipped the glycerin altogether because it gave us a strange residue that resembled a spider web.

256 oz. of HEB Orange or Lemon Liquid Dish Soap  (it gave the water a nice pleasing color)

7 gallons of Ozark’s Distilled Water

(Still inspired by Frei Otto’s soap recipe.) (Nerdinger, page 19)

4 feet by 1-foot tank for our large model

25 to 40 feet of 18-gauge Copper wire

18 w to 30 w soldering device

Soldering Wire

A ruler

Masking tape


4 feet by 1 feet wooden box


Plumbers clear caulk

Our Experiment:

This week we focused on our model at a larger scale.   We focused on reducing our model to maybe 10 to 12 nodes.   These nodes have initially 4 large parallelograms.   Some of the parallelograms began at a bigger size, and as we progressed or made the model longer, we began to change the size of the parallelograms, until they became small in size.

This approach helped us play with symmetry, hierarchy (since we went from large to small shapes).  It also gave us datum, axis, repetition, and transformation (we did change the size of the shapes).

It also gave us a chance to explore the approach to the structure or configuration of a path since you can enter from either end and walk underneath the structure.   Its shape provides enough volume to visually guide people in two or four directions.   The diagonal masts also provide another point of entry where the museum patrons could join others as they are walking through the installation.  Yet, we are still at a very conceptual stage.

Jan 29, 2014 - Presentation model

Jan 29, 2014 – Presentation model

We soldered copper wire together along with silver soldering wire-making squares big and small (2 ½ by 2 ½ inches square) or either 1 by 1 inches square.    These squares were later bent and made into a shape that looked like two intercepted triangles or parallelograms.

Longitudinal view our our Presentation Model - Jan 29, 2014.

Longitudinal view our our Presentation Model – Jan 29, 2014.

We built a 4 feet by 1 foot wooden box that was screwed, sanded and sealed using polyurethane, and plumber’s transparent caulk.   Then, filled it with soap and water, dipped our model in the wooden tank and presented our soap film model to the class and to our instructor.

Another longitudinal view. Jan 29, 2014.

Another longitudinal view. Jan 29, 2014.

Detail of the Soap Film tents. Jan 29, 2014.

Detail of the Soap Film tents. Jan 29, 2014.

This time the model supported itself, because the parallelograms became the mast for support giving it its conceptual shape.

Andres Mulet                  Aleksandr Mikhailov                    Troy O’Connor

(The Minimal Surfaces Group).


Kaw, Autar and Snyder, Luke, Differentiation of Continuous Functions, College of Engineering, University of South Florida – – February 1, 2014  (accessed Feb 1, 2014).

King, Andrew J., and David J. T. Sumpter. 2012. Murmurations. Current Biology 22, (4): R112-R114, (accessed February 1, 2014).

Pitkin, Joe. “A Murmuration of Starlings.” Analog Science Fiction & Fact 132, no. 6 (06, 2012): 42-50.

%d bloggers like this: