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Ruth Asawa

Ruth Aiko Asawa (1926 - 2013) was an American artist known primarily for her looped-wire sculptures. Born in Norwalk, California Asawa was the daughter of Japanese immigrants. She grew up on a truck farm. Between 1946 and 1949 Asawa studied at the Black Mountain College. In 1955, she held her first exhibition in New York and by the early 1960s, she had achieved commercial and critical success. Her work is featured in major international museums. In 2020, the U.S. Postal Service honored her work by producing a series of ten stamps.

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Ruth Asawa with hanging sculpture, 1952. Photo by Imogen Cunningham

Black Mountain College

In 1946, Asawa joined the Black Mountain College. The College was a progressive experiment that would last only 24 years. Conceived by faculty from other colleges and an advisory board that included John Dewey, Albert Einstein, Walter Gropius and Carl Jung, the college opened in rural North Carolina in 1933.

"I spent three years there and encountered great teachers who gave me enough stimulation to last me for the rest of my life - Josef Albers, painter, Buckminster Fuller, inventor, Max Dehn, the mathematician, and many others." Buckminster Fuller arrived in the summer of 1948 with "his magical world of mathematical models packed in an aluminum trailer." Asawa is quoted on her website.

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Buckminster Fuller (Mid) and Josef Albers (left background) with students at Black Mountain College, summer 1948: Construction of a geodesic dome.

Wiring techniques

It was because of her material lessons from Josef Albers that Asawa discovered a new use for wire on a visit to Mexico in 1947. A craftsman in Toluca showed her how he made egg baskets by looping wire. She would later elevate this technique from functional baskets to her looped-wire sculptures. Here are some traditional weaving techniques that look similar to Asawa's wire work:

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Daniel Sutherland Davidson, “Knotless Netting in America and Oceana”, 1935

We can see Asawa's netting technique in her below untitled sculpture:

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Organic forms

Shortly after her trip to Mexico, Asawa sketched figures that resembled her later biomorphic sculptural forms

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Ruth Asawa, Exercise in color vibration and figure background, 1948, Harvard Art Museums

My attempt

My own attempt to construct looping mesh patterns wasn't too successful. Probably the plot would look better if we could rotate the horizontal mesh loops by 90 degrees, but I couldn't find a way to do so.

s = 0.05;
w = 40;

default =
  ParametricPlot3D[
   {Cos[u] Sin[v] + s Sin[w (u + v)],
    Sin[u] Sin[v] + s Cos[w (u + v)],
    2 Cos[v]},
   {u, 0, 2 Pi}, {v, 0, Pi},
   Mesh -> 12,
   MeshStyle -> Gray,
   PlotLabel -> "Default View",
   PlotPoints -> 64,
   PlotStyle -> None];

front =
  Show[default,
   Axes -> False,
   Boxed -> False,
   PlotLabel -> "Front View",
   ViewPoint -> Front];

GraphicsRow[{default, front}, Frame -> All, FrameStyle -> LightGray]

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My question

How can we reproduce wired Asawa - forms? More of them can be seen here on her website. I would also accept 2-dimensional solutions (using splines?) if they create an "illusion of depth" by placing smaller forms inside larger ones like in the image below.

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Ruth Asawa in 1954

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1 Answer 1

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An attempt in 2D:

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s = .05; w = 50;
p1 = ParametricPlot[
  {.8, .5} {Cos[u] Sin[v] + s Sin[w (u + v)], Cos[v] + s Sin[v]}, {u, 0, 2  Pi}, {v, 0, Pi}
  , Mesh -> {80, 0},MeshStyle -> Directive[GrayLevel[.4], AbsoluteThickness[1.8]]
  , PlotPoints -> 80,  PlotStyle -> None, BoundaryStyle -> None, MaxRecursion -> 3];

p2 = ParametricPlot[
  {0, -.0} + {.4, .35} {Cos[u] Sin[v] + s Sin[w (u + v)], Cos[v] + s Sin[v]}, {u, 0, 2 Pi}, {v, 0, Pi}
  , Mesh -> {80, 0}, MeshStyle -> Directive[GrayLevel[.2], AbsoluteThickness[1.8]]
  , PlotPoints -> 80,  PlotStyle -> None, BoundaryStyle -> None, MaxRecursion -> 3];

p3 = ParametricPlot[
  {0, -.6} + {.55, .45} {Cos[u] Sin[v] + s Sin[w (u + v)], Cos[v] + s Sin[v]}, {u, 0, 2 Pi}, {v, 0, Pi}
  , Mesh -> {80, 0}, MeshStyle -> Directive[GrayLevel[.7], AbsoluteThickness[1.8]]
  , PlotPoints -> 80,  PlotStyle -> None, BoundaryStyle -> None, MaxRecursion -> 3];

p4 = ParametricPlot[
  {0, -.85} + {.3, .25} {Cos[u] Sin[v] + s Sin[w (u + v)], Cos[v] + s Sin[v]}, {u, 0, 2 Pi}, {v, 0, Pi}
  , Mesh -> {80, 0}, MeshStyle -> Directive[GrayLevel[.2], AbsoluteThickness[1.8]]
  , PlotPoints -> 80,  PlotStyle -> None, BoundaryStyle -> None, MaxRecursion -> 3];

p5 = ParametricPlot[
  {0, .5} + {.4, .35} {Cos[u] Sin[v] + s Sin[w (u + v)], Cos[v] + s Sin[v]}, {u, 0, 2 Pi}, {v, 0, Pi}
  , Mesh -> {80, 0}, MeshStyle -> Directive[GrayLevel[.5], AbsoluteThickness[1.8]]
   , PlotPoints -> 80, PlotStyle -> None, BoundaryStyle -> None, MaxRecursion -> 3];

Show[
  Graphics[{  
     GeometricTransformation[p5[[1]], RotationTransform[-Pi/24, {0, .5}]]
   , GeometricTransformation[p1[[1]], RotationTransform[Pi/64, {0, 0}]]
   , GeometricTransformation[p2[[1]], RotationTransform[Pi/48, {0, 0}]]
   , GeometricTransformation[p3[[1]], RotationTransform[-Pi/64, {0, 0}]]
   , GeometricTransformation[p4[[1]], RotationTransform[Pi/48, {0, -1}]]}
  , PlotRange -> All, ImageSize -> Medium]]
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