Square Limit by M.C. Escher

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Square Limit by M.C. Escher

• How are the fish in the middle of the design and
  the surrounding fish alike?
• How are they different?

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Square Limit by M.C. Escher

• Escher used a pattern of squares and triangles to
  create Square Limit.

• These two triangles are similar.

• Similar figures have the same shape but not
  necessarily the same size.

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One way to create artwork with a smaller and
smaller framework is to base it on an isosceles
triangle with an apex angle whose measure divides
360º evenly.
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We have elected to base our artwork on an
isosceles triangle with an apex angle of measure
45º where 360º/45º 8. An octagonal
configuration will result.
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Select the midpoint of the base of the triangle.
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Add a row of five similar smaller triangles by
drawing line segments parallel to the slant sides
of the triangle.
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The result is the basis of the shrinking
repeating fundamental unit.
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Add a continuous curve from vertex to vertex of
one of the sides of the original triangle.
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Rotate this curve about the apex of the original
triangle to its congruent side.
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Draw reductions of this curve from vertex to
vertex of each of the four reduced line segments
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This is the shrinking tessellating unit.
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Add interpreting interior features.
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Continue the reduction algorithm indefinitely
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Continue the reduction algorithm indefinitely
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Continue the reduction algorithm indefinitely
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Continue the reduction algorithm indefinitely
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Continue the reduction algorithm indefinitely
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Continue the reduction algorithm indefinitely
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then add the tessellating unit with its
interpreting features and reductions thereof as
required.
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then add the tessellating unit with its
interpreting features and reductions thereof as
required.
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then add the tessellating unit with its
interpreting features and reductions thereof as
required.
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