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?

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.

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.

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.

Select the midpoint of the base of the triangle.

Add a row of five similar smaller triangles by drawing line segments parallel to the slant sides of the triangle.

The result is the basis of the shrinking repeating fundamental unit.

Add a continuous curve from vertex to vertex of one of the sides of the original triangle.

Rotate this curve about the apex of the original triangle to its congruent side.

Draw reductions of this curve from vertex to vertex of each of the four reduced line segments

This is the shrinking tessellating unit.

Add interpreting interior features.

Continue the reduction algorithm indefinitely …

… then add the tessellating unit with its interpreting features and reductions thereof as required.