title: Fractals: Endlessly Repeated Geometrical Figures
author: Hans Lauwerier
description: <b>&quot;One of Choice&#39;s Outstanding Academic Titles for 1992&quot;</b><br /><br />"This is a valuable, attractive and unpretentious introduction to a fascinating subject." (<i>American Scientist</i>)
zlib_text: 45
  Chapter 6
  Examples
  The view taken here is that “an example is worth a thousand words”. One of the claims made is that one can 
   fractalize with a fill region of any shape. While a formal proof of that seems remote, a large number of examples 
  makes it plausible. The examples given here have both mathematical and artistic features. The application of the 
  algorithm to art has been treated in several papers by Dunham and Shier [9–11].
  Figure 6.1 shows fractalization of two semicircles on the left. One has the flat side up, the other the flat side 
  down. The artist can ask “What recognizable objects can these be?” The answer illustrated here is that they can be 
  eyes and mouths. One can assign a surrealistic title like “How Dali remembered the girlfriends of his youth”.
  The targets of Fig. 6.2 are constructed using three circles, and c is close to its upper limit. The radii are chosen 
  such that six smaller targets can fit exactly in the annular space within a target. What is interesti