Tag Archives: rose window

Rosettes with glide reflection and rotation symmetry

We now come to the last distinct combination of symmetries for friezes and rosettes. It uses the glide reflection and the rotation by 180 degrees resulting from two mirror symmetries of the two preceeding posts. The mapping functions have to have the symmetry … Continue reading

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rosettes with glide reflection

For a rosette of p-fold rotational symmetry you have an equivalent to the glide reflection symmetry of a fries. It is a rotation by an angle of π/p around its center together with a reflection or  rather inversion at r=1. … Continue reading

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Combinations of mirror symmetries

We now create rosettes with combinations of the two mirror symmetries. We can put them in “parallel” or in “series”. In “parallel” means that the rosette has both symmetries at the same time and thus the mapping functions have to obey … Continue reading

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tired of rhombs ?

Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading

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Cellular automaton on quasiperiodic tiling

Any tiling can be used to define a cellular automaton. The tiles (squares, triangles, rhombs and other polygons) are simply the cells. Each tile has all other tiles with a common edge in its von Neumann neighborhood. I use the … Continue reading

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anamorphosis with 6-fold rotational symmetry

Thinking of snowflakes I made anamorphic images with 6-fold rotational symmetry based on the 6th power of z=x+iy. But because of the strong distortions I could not get anything resembling the crystalline beauty of snowflakes. Instead I got somewhat amorphous … Continue reading

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An iterative hexagonal kaleidoscope

We can use the geometry of the last post differently. Draw inside a hexagon two equal sided triangles with the same corners as the hexagon. Then the intersection between the triangles gives a new smaller hexagon. Repeating this we get … Continue reading

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