Tag Archives: Geometry

Curves

Frank Farris begins his book “Creating Symmetry” with symmetric curves of N-fold rotational symmetry. An example: He uses that we can interpret points (x,y) of the plane as complex numbers z=x+i*y. Thus a complex function f(t) of a real parameter t defines … Continue reading

Posted in Kaleidoscopes, programming | Tagged , , , | 2 Comments

Creating Symmetry

Recently I found a very exciting book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris. It has many beautiful images and explains the mathematics behind them very well, such that you could do your own work. His … Continue reading

Posted in Kaleidoscopes, Tilings | Tagged , , , , | Leave a comment

Geometry of kaleidoscopes with periodic images

About a year ago I explained “how to program an ideal kaleidoscope” to get the same as three mirrors put together. Often, one gets images that are not periodic. They have cut lines with a mismatch between the two sides, … Continue reading

Posted in Kaleidoscopes | Tagged , , , , , | 2 Comments

improved class Vector – the code

// a class for two-dimensional vectors, similarly as PVector, with extensions for complex numbers //————————————————————- // //  some important values float vectorSmall=0.0001; float vectorDiameter=8; color vectorColor=color(255);      //  and here’s the class class Vector{   float x,y;     // … Continue reading

Posted in programming, Uncategorized | Tagged , , | Leave a comment

improving the class Vector

I am not happy with my class Vector. Looking at my posts “Nautilus” and “self-similar fractals …” I realize that complex numbers and vectors should be put together with their methods, which are mostly mappings of the plane. In particular, … Continue reading

Posted in programming, Uncategorized | Tagged , , | Leave a comment

high resolution images with off-screen drawing

In an earlier post I have shown how to make smooth images at any scale using the pdf-renderer. But you can do this only with graphics objects such as line, point, shape, ellipse and so on. It won’t work if … Continue reading

Posted in Anamorphosis, Cellular automata, Extra, Fractals, Kaleidoscopes, programming | Tagged , , , , , | Leave a comment

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

Posted in Quasiperiodic design, Tilings | Tagged , , , , , | Leave a comment