Spirals

spring rollIt is Winter now, but Spring is right around the corner. Looking back at this picture of a tulip, unfurling from the ground in front of my house a few Aprils ago, got me thinking about spirals.

Many living things, both plants and animals, share this form in their growth patterns. Haeckel_Ammonitida

This plate from Art Forms of Nature  by German biologist Ernst Haeckel shows examples of ancient Ammonitida shells. I marvel at their complexity and perfection.

No less amazing is M74, the Perfect Spiral Galaxy, a spectacular example of a “grand design spiral galaxy.”

m74_baixauli_900

Fibonacci numbers describe these spiral phenomena mathematically.

Fibonacci_spiral_34.svg

There are many works of architecture based on the spiral, from whole buildings to details, to spiral staircases.

There is a special spiral staircase in Baker Hall, at my alma mater, Carnegie-Mellon University (CMU), built with nothing but layered thin Terra-cotta tiles, as a variation of timbrel vault type of construction.

2012_11_12_images_10_guastavini

It supports itself without a steel armature, posts or beams.  The sinuous gentle curve is gorgeous. The a herringbone tile pattern along the curved underside is one of three layers of tile adhered together with fast-setting mortar.  The resulting laminated shell is almost as strong as reinforced concrete.

It was built by the company of a Spanish master builder, Rafael Guastavino, who excelled at designing and building timbrel arches, vaults, and spiral stairs. Guastavino structures, unlike Roman arches and vaults, don’t require heavy wooden supports (centering) during their construction. “The Guastavino craftsmen could start at the four walls of a room and build toward the center. The masons could stand on a ladder or a platform, but they didn’t have to build a wooden frame to support their structure while it was being built—it almost seems miraculous…We have a difficult time today calculating the geometries of (this) structure. I have students here at MIT doing doctoral research, trying to understand how these structures stand up. We can’t build this staircase today.””

The above quote is from MIT structures Professor John Ochsendorf in “Vaulting Ambition,” by Craig Lambert, in Humanities Magazine, a great article that explores the Guastavino’s history, work and influence.

There is an upcoming exhibit in the National Building Museum, called Palaces for the People: Guastavino and America’s Great Public Spaces, which will be on view from March 16, 2013 to January 20, 2014. I hope to get a chance to see it.

The first photo is mine; the second photo is courtesy of Wikimedia Commons; the third photo is courtesy of NASA; the fourth photo is courtesy of Wikipedia; and the fifth photo is courtesy of Michael Freeman.

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Print Making Venture

I’ve been enthusiastically making prints lately!  Please check them out at this link:

LK PRINTS

Umami 1

All Images courtesy of Laura Kraft.

Feel free to share any of these copyright-protected images, but please provide a link back to 2H Pencil.

I invite your comments.

Asymmetry

450px-Chartres_1

Chartres Cathedral

Asymmetry is literally a lack of symmetry. It is usually defined in negative terms such as “objects that are not identical on both sides of a central line,” or those having a “failure of parts to correspond to one another in shape, size, or arrangement.“  It has been described as distorted, disquieting, out of place, hyperactive, tiresome, and threatening.

This blog post is a consideration of asymmetry in positive terms.

1.  Asymmetrical objects cause our eyes to actively scan, and our minds to actively evaluate the unequal parts of the form, seeking balance.  I feel this active engagement as stimulation, engagement, and fascination. Sometimes, a dynamic balance is achieved in an object; sometimes it is not.

2.  In addition to being a source of formal interest, asymmetry can deliver vital information. There are examples of extreme asymmetry in living things, such as this type of flounder, which has both eyes on the right side of its body. Other species of flounder are known to have both eyes on the left side of their bodies.  This is functional for them because they live at the bottom of the sea with enormous pressures causing them to lie flat.
Kuvalähde: Wilhelm vonWright: Pohjolan kalat.
CrabGross asymmetry such as that of the fiddler crab above can tell a story about a creature’s role, functioning, or habitat.  It raises the question, “What are the functional reasons for this particular form?”

3. There are degrees of symmetry. The human face is generally symmetrical, with 2 eyes, 2 nostrils, 2 cheeks, and 2 eyebrows. Yet on closer inspection of almost every face, inequality of the parts is obvious. Asymmetry is the source of interest, beauty, ugliness, and expression.

b849cc4f3f3cbfd185a6d84c47da75c6_6

Marilyn Monroe’s iconic and memorable face (top center) is admired. By mirroring just the left side (lower left), and comparing that to a mirroring of only the right side (lower right), we can see that it is far from symmetrical in structure and detail. Her facial imbalance gives her vulnerability and compelling beauty. She even darkened her beauty mark to enhance the irregular composition.

4. For human-made things, composition is a result of choices. What is the meaning or message in the choice to “go crooked?” In the early 1900s, Kazimir Malevich, a Russian Suprematist artist, created elemental, abstract art, which was shocking and radical in its time.

 malevich.black-red-square
malevich.petersburg
Here are some famous examples of architecture in which, as described in the four points above, asymmetry :
1. stimulates active engagement opening the possibility of stimulation and fascination.
2. raises questions about the functional reasons for its particular form.
3. is the source of interest, beauty, ugliness, and expression.
4. raises questions about the meaning or message in the choice to “go crooked”

800px-Thomas_Crane_Public_Library,_Quincy,_Massachusetts_(Front_view)

Thomas Crane Public Library by H.H. Richardson, 1882.

asymmetry-architecture-beauty

Auditorio de Tenerife by Santiago Calatrava, 2003

fallingwater

Fallingwater by Frank Lloyd Wright, 1939

lotheringen_12

Coetzee House by Emilio Eftychis, 2005(?)

Niterói_Contemporary_Art_Museum

Niteroi Contemporary Art Museum by Oscar Niemeyer, 1996.

Miyakonojo 2

Miyakonojo Civic Center in Miyakonojo, by Kiyonori Kikutake, 1966, Metabolist Architecture

Chartres Cathedral image courtesy of Wikipedia.

First photo of a flounder courtesy of TBD; second image of a fiddler crab courtesy of Google Images; third image of Marilyn Monroe courtesy of upscale; images of Malevich paintings courtesy of Web Museum.

First architectural example courtesy of Wikipedia, second courtesy of  Wikipedia; third courtesy of fallingwater.org; fourth courtesy of designboom; fifth courtesy of Wikepedia; sixth courtesy of Panaramio.

Feel free to share any of these images, but please provide a link back to 2H Pencil.

I invite your comments.

Spirals

spring rollSpring is beginning to happen. This tulip, unfurling from the ground in front of my house, got me thinking about spirals.

Many living things, both plants and animals, share this form in their growth patterns. Haeckel_Ammonitida

This plate from Art Forms of Nature  by German biologist Ernst Haeckel shows examples of ancient Ammonitida shells. I marvel at their complexity and perfection.

No less amazing is M74, the Perfect Spiral Galaxy, a spectacular example of a “grand design spiral galaxy.”

m74_baixauli_900

Fibonacci numbers describe these spiral phenomena mathematically.

Fibonacci_spiral_34.svg

There are many works of architecture based on the spiral, from whole buildings to details, to spiral staircases.

There is a special spiral staircase in Baker Hall, at my alma mater, Carnegie-Mellon University (CMU), built with nothing but layered thin Terra-cotta tiles, as a variation of timbrel vault type of construction.

2012_11_12_images_10_guastavini

It supports itself without a steel armature, posts or beams.  The sinuous gentle curve is gorgeous. The a herringbone tile pattern along the curved underside is one of three layers of tile adhered together with fast-setting mortar.  The resulting laminated shell is almost as strong as reinforced concrete.

It was built by the company of a Spanish master builder, Rafael Guastavino, who excelled at designing and building timbrel arches, vaults, and spiral stairs. Guastavino structures, unlike Roman arches and vaults, don’t require heavy wooden supports (centering) during their construction. “The Guastavino craftsmen could start at the four walls of a room and build toward the center. The masons could stand on a ladder or a platform, but they didn’t have to build a wooden frame to support their structure while it was being built—it almost seems miraculous…We have a difficult time today calculating the geometries of (this) structure. I have students here at MIT doing doctoral research, trying to understand how these structures stand up. We can’t build this staircase today.””

The above quote is from MIT structures Professor John Ochsendorf in “Vaulting Ambition,” by Craig Lambert, in Humanities Magazine, a great article that explores the Guastavino’s history, work and influence.

There is an upcoming exhibit in the National Building Museum, called Palaces for the People: Guastavino and America’s Great Public Spaces, which will be on view from March 16, 2013 to January 20, 2014. I hope to get a chance to see it.

The first photo is mine; the second photo is courtesy of Wikimedia Commons; the third photo is courtesy of NASA; the fourth photo is courtesy of Wikipedia; and the fifth photo is courtesy of Michael Freeman.

Feel free to share the content of this blog, but please provide a link back to 2H Pencil.

I invite your comments.

Illusions, No. 2

The impulse to challenge users and viewers has long been at the heart of trompe l’oeil (fool the eye) projects. When the eye sees something, the body believes it.

Two-dimensional patterns (made with tiles, carpet, paint, or…..) can create the optical illusion of three dimensionality.

Image

In the pattern above, do you see stacked cubes with white tops? Or white bottoms?  Does the image change back and forth for you?

pattern 7

Here, the colors are rearranged. Is the white surface the top, right, left, or bottom of the cube?

Image

Does this pattern look flat or 3-D? Do you see square holes or pyramids?

Pattern 2

Is this arrangement actually possible in three dimensions?

L Accademia

This sketch of the floor pattern at the Accademia Museum in Venice shows square “recesses” in the medallion on the right, anchored in a flat peach-colored field.  The 3-D illusion is contained, and I don’t fear falling through this floor.

82962747_4cb33a8ac4

Would this give you vertigo?

Golden_Staircase400

Would this stair landing make you pause before walking on it?

GEORGE-WINTERINGHAM_LISBONPAVING3

Can you feel the surface ripple?

3D-Optical-Illusion-Carpet

Does this (actually flat) carpeting make you want to stagger? Or worse?

warped

A computer-generated tile design clads these perfectly flat and plumb surfaces. Architect Thom Faulders‘ client said, “I wanted someone to barf when they look at it.” This illusion, versus the reality of its flatness, comes close!

The first five drawings were made by me. The first and second photos’ attributions are TBD; the third photo is courtesy of George Winteringham, via Patternity; the fifth photo is courtesy of Vurdlak; the sixth photo is courtesy of Thom Faulders.

Feel free to share the content of this blog, but please provide a link back to 2H Pencil.

I invite your comments.

Symmetry

Like butterflies, most other animals, and some plants,

we humans possess bilateral symmetry. We have a center line, with basically the same stuff on the right and the left.

Researchers of social psychology essentially agree that the faces we find most alluring are also the most symmetrical ones. To be physically balanced on either side of a center line is considered a primal hallmark of health and, therefore, beauty.

Just as we viscerally relate to symmetrical living beings, we relate to symmetrical objects.  We can discern a center line, and in general, we expect to see the same stuff on the right as on the left. There is a “rightness” to well-designed symmetrical architecture.

Symmetry is apt for expressing structural forces.

It imparts gravitas and elegance when used to mark transitions.

1940-packard-160-front

 It can give objects a human aspect.

 Sometimes, for better or worse, the quest for symmetry can cause a building’s exterior appearance to take precedence over what the interior spaces need or want to be.

metro paris

A design needn’t be an exact mirror image to be symmetrical.

Symmetry can be as simple and serene as a blanket folded in two over a pole.

First photo of a Monarch butterfly courtesy of Karenswhimsy.com ; second image of Cattleya walkeriana orchid courtesy of Greg Allikas; third image of Vitruvian Man courtesy of Leonardo DaVinci; fourth image of the Eiffel Tower courtesy of Wikepedia; fifth image of a Torii Gate courtesy of Kate Comings; sixth image of The Dime Savings Bank of Brooklyn courtesy of My Bank Tracker; seventh image of 1940 Packard 160 courtesy of Hyman Ltd.; eighth image of Parisian Art Nouveau entrance courtesy of Traveling Squire; ninth image of pup tent courtesy of Imgfave.

Feel free to share any of these images, but please provide a link back to 2H Pencil.

I invite your comments.