VISUAL PERMUTATIONS: TOWARDS 2D 
AND 3D SYMMETRIES AND FRACTALS

PART 2

JUDITH NEMís


 

4 FRACTAL SYMMETRY

The same visual words as defined by the random permutations outlined in Part 1 are used to further the concept of symmetry to understand the visual impact of scaling. A simple imbedding algorithm is applied to create visual meta-words that could in turn be used to generate (meta) sentences similarly to the approach described in Section 3 of Part 1. These imbedded words could then be used to analyze the impact of up/down scaling. Figure 7 shows the case of central fractal symmetry while Fig. 8 illustrates that of skewed fractal symmetry. In both case the same self-similarity principle has been used.

.


 

Figure 7
 
 


 

Figure 8





5 THE THREE-DIMENSIONAL CASE
 
 

         
 
 

Figure 9                             Figure 10

The very same principles are used in the 3D case. These hanging columns (függvény in Hungarian, dependent in English), shown in Fig 9 and 10, attempt to generalize what has been put forth in the preceding sections.
 
 

Acknowledgement. The author is indebted to Mr. András Szöllasi-Nagy for his advice and continuous moral support throughout the work of this research project. 
 
 

References

Lin, Shu-Kun (2001) The nature of the chemical process: 1. Symmetry evolution Ė Revised information theory, similarity principle and ugly symmetry, International Journal of Molecular Science, 2, 10-39.