# Tag Archives: anamorphosis

## The rotational and mirror symmetry at the center

In the last post I used mirror symmetry at two crossing straight lines and the related inversion at a circle. The mirror symmetries generate a k-rotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading

## Morphing between square symmetry and eight fold rotational symmetry

A long time ago in “Crazy graph paper” I have shown a morphing between the square lattice and the quasiperiodic Ammann-Beenker tiling of eight-fold rotational symmetry. We can do similar morphs with mapping functions using waves. The wave vectors (1,0) … Continue reading

## Self-similarity and color modification

The Penrose tiling is self-similar as many other quasi-periodic tilings. It matches a copy of itself inflated by the golden ratio τ=(1+√5)/2≅1.618, see “Penrose tiling tied up in ribbons“. Noting that our quasi-periodic designs of 5-fold symmetry are closely related to … Continue reading

## Spirals

Spiral designs are attractive and we can easily get them by transforming periodic designs. An example is the “Iris Spiral” created by Frank Farris. In my earlier post “Nautilus” I tried to explain the method and showed some results. Unfortunately, … Continue reading

Posted in Anamorphosis, Kaleidoscopes | | 1 Comment

## Better images from higher harmonics ?

Maybe you have noticed that a lot of round shapes without details in the recent images of this blog. They resemble bulls-eyes. Here is an example: It’s a periodic image with square symmetry and no mirror symmetry. Its big grey … Continue reading

## 2-color mirror symmetry

We now want an image with periodic or quasi-periodic rotational symmetry that changes colors upon mirroring. Thus we need a color-changing function U(x,y) that changes the sign U(x,-y)=-U(x,y) for its mirror image at the x-axis. We can easily get this … Continue reading

## Mirror symmetry and rotational symmetry

To study mirror symmetry at the x-axis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading

## Improved two-color symmetry upon rotation

As discussed in the post “two-color rotational symmetry” we get only a single real color-changing function U(x,y) instead of a mapping W(x,y)=U(x,y)+iV(x,y) to the complex plane. Thus we need a special approach to get a mapping to the input image … Continue reading

## improved combination of color symmetry and rotation

As mentioned in the last post using two unrelated anamorphic mappings, one for reading the input image and another one for choosing color variants, makes it difficult to create interesting images. From the mapping that determines the color variant we … Continue reading

## three-color rotational symmetry

I found it rather difficult to add three-color symmetry to rotational symmetry and had to do the theory of the post “color symmetry upon rotation“. Then, programming was quite easy.  In the end we combine a periodic or quasi-periodic anamorphic … Continue reading