# Tag Archives: generative design

## Numerical performance

Curves do not need much calculations and are easy to generate. Rosettes, friezes and kaleidoscopes are different. They need many calculations for each pixel, often using several evaluations of trigonometric functions and exponential functions. Fortunately, our PCs are fast. A … Continue reading

## 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 | | 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

## Self-similar images from iterated mappings of the plane

A mapping of the plane defines simply another point (u,v) in the plane as a function of the coordinates (x,y) of a point in the plane. The mapping is defined by the functions for the new coordinates u=f(x,y) and v=g(x,y). … Continue reading

## cellular automaton with color on a square lattice

I used the same methods as in the last post but now for a square lattice. I could not get similar results with 4-fold rotational symmetry instead of 6-fold rotational symmetry. Instead, the images were rather different. For my taste, … Continue reading