Quelltext der Seite Flowsnake Earth


== Referenz == 
Jacob Rus: [[Flowsnake Earth]]. In: [[Bridges 2017]], Pages 237–244. 

== DOI ==

== Abstract ==
By folding and gluing the edges of a collection of one or more regular hexagons, there are several ways to build closed polyhedra. The surface of the sphere can be mapped conformally to the faces of these polyhedra, and therefore onto the hexagons. The Gosper island is a two-dimensional fractal shape generated from a hexagon which seamlessly tiles the plane in a triangular lattice, and can be recursively subdivided into 7 congruent Gosper island shapes similar to the original. The flowsnake is a space-filling fractal curve which fills the Gosper island. When we combine these ideas we can construct several map projections from the sphere onto a collection of Gosper island shapes, each yielding as an inverse a “sphere-filling” fractal curve, and a recursive subdivision of the sphere into smaller Gosper island shapes in a succession of triangular lattices. 

== Extended Abstract ==

== Bibtex == 
 @inproceedings{bridges2017:237,
  author      = {Jacob Rus},
  title       = {Flowsnake Earth},
  pages       = {237--244},
  booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
  year        = {2017},
  editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
  isbn        = {978-1-938664-22-9},
  issn        = {1099-6702},
  publisher   = {Tessellations Publishing},
  address     = {Phoenix, Arizona},
  note        = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-237.pdf}}
 }

== Used References == 
[1]
J. P. Snyder. Map projections: A working manual. Vol. 1395. USGPO, 1987. https://pubs.er.usgs.gov/publication/pp1395

[2]
E. S. Popko, Divided Spheres. CRC press, 2012. http://www.dividedspheres.com

[3]
L. Middleton and J. Sivaswamy. Hexagonal Image Processing. Springer, 2006.

[4]
A. Lösch. Economics of Location. Yale, 1954.
http://archive.org/stream/economicsoflocat00ls#page/110

[5]
N. Sloane. A003136, “Löschian numbers.” OEIS. 2017.
https://oeis.org/A003136

[6]
M. Goldberg. “A class of multi-symmetric polyhedra.” Tohoku Math. J., First Series 43, 1937: 104–108.
https://www.jstage.jst.go.jp/article/tmj1911/43/0/43_0_104/_pdf

[7]
M. Gardner. “Mathematical Games.” Scientific American 235, 1976: 124–133.
https://scientificamerican.com/article/mathematical-games-1976-12/

[8]
J. Ventrella. Brainfilling Curves. Lulu.com, 2012. http://fractalcurves.com

[9]
R. J. Purser and M. Rančić. Office Note 467. NOAA, 2011.
http://www.lib.ncep.noaa.gov/ncepofficenotes/files/on467.pdf

[10]
S. Pérez-Duarte and D. Swart. “The Mercator Redemption.” Proc. Bridges, 2013: 217–224.
http://archive.bridgesmathart.org/2013/bridges2013-217.html

[11]
T. Needham. Visual Complex Analysis. Oxford, 1997. http://usf.usfca.edu/vca

[12]
T. Driscoll and L. N. Trefethen. Schwarz–Christoffel Mapping. Cambridge, 2002. http://www.math.udel.edu/~driscoll/SC

[13]
K. Sahr, D. White, and A. J. Kimerling. “Geodesic discrete global grid systems.” Cartogr. Geogr. Inf. Sci., 30(2), 2003: 121–134.
http://www.discreteglobalgrids.org/publications

[14]
G. Irving and H. Segerman. “Developing fractal curves.” J. Math. Arts 7(3–4), 2013: 103–121. http://www.3dprintmath.com

[15]
R. Fathauer. “Radial Development.” 2014.
http://robertfathauer.com/SphericalCurveSculp.html

[16]
J. Sullivan. “Conformal Tiling on a Torus.” Proc. Bridges, Coimbra, 2011: 593–596. http://archive.bridgesmathart.org/2011/bridges2011-593.html

[17]
D. M. German et al. “Flattening the Viewable Sphere.” Computational Aesthetics, 2007: 23–28. http://dl.acm.org/citation.cfm?id=2381258

== Links == 

=== Full Text === 
http://archive.bridgesmathart.org/2017/bridges2017-237.pdf

[[internal file]] 


=== Sonstige Links ===