Creating Self Similar Tiling Patterns and Fractals using the Geometric Factors of a Regular Polygon

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Reference

Stanley Spencer: Creating Self Similar Tiling Patterns and Fractals using the Geometric Factors of a Regular Polygon. In: Bridges 2014. Pages 279–284

DOI

Abstract

A regular polygon with n sides can always be decomposed into isosceles triangles chosen from a set of k non- similar isosceles triangles where k is the integer part of (n-1)/2. It appears that the set displays a property I have, in previous papers, called preciousness. This implies that each triangle in the set can be decomposed into assemblies of uniformly scaled triangles chosen from the set. This process can be repeated and forms the basis of recursive tilings and fractals depending upon the details of the process. The value of n has an effect on the symmetry of the design. The relationship between two different regular polygons where the number of sides of one is a factor of the other is also explored. Isaac Newton once famously said that he could see further because he was able to stand on the shoulders of earlier giants. As a theme for decorating the designs I have created pictures of his giants. I have also included pictures of Newton and Einstein as being giants in their own right.

Extended Abstract

Bibtex

Used References

[1] Goodman A.W. and Ratti J.S., Finite Mathematics with Applications - pp. 82-89. 1971 Macmillan - before ISBN

[2] http://www.keithschwarz.com/interesting/code/?dir=factoradic-permutation(as of Nov. 15, 2013)

[3] http://jamesmccaffrey.wordpress.com/2012/09/07/the-factoradic-of-a-number(as of Nov. 15, 2013)

[4] Spencer S J, The Tangram Route to Infinity pp. 52-57 for matrix notation and appendix 6 for eigen values

[5] Spencer S J, Alhambra. Bridges 2003 Proceedings pp. 291-298 An introduction the tiling properties of precious triangles.

[6] Spencer S J, Kansas. Bridges 2004 Proceedings pp. 71-78 The tiling properties of the tangram

[7] Spencer S J,Banff. Bridges 2005 Proceedings pp. 31-36 An introduction to the golden tangram and its tiling properties.

[8] Spencer S J, London. Bridges 2006 Proceedings pp. 73-78 Introducing the precious tangram family.

[9] Spencer S J,Towson. Bridges 2012 Proceedings pp. 337-334 Introducing the use of primary isosceles triangles of regular polygons.

[10] http://en.wikipedia.org/wiki/Lehmer code(as of Nov. 15, 2013)

[11] http://en.wikipedia.org/wiki/Factorial number system(as of Nov. 15, 2013)


Links

Full Text

http://archive.bridgesmathart.org/2014/bridges2014-279.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2014/bridges2014-279.html