Abstract
We report on computer search for generalized Gosper curve for 37 < N < 61, where N is the degree of the generalized Gosper curve. From the results of the computer search and some geometrical insight, we conjecture that the degree N satisfies N = 6n + 1. We investigate the existence of infinite series of generalized Gosper curves. We show how to generate these series and introduce two new methods, the ‘decomposition method’ and the ‘modified layer method’.
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© 2007 Springer Berlin Heidelberg
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Akiyama, J., Fukuda, H., Ito, H., Nakamura, G. (2007). Infinite Series of Generalized Gosper Space Filling Curves. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_1
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DOI: https://doi.org/10.1007/978-3-540-70666-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70665-6
Online ISBN: 978-3-540-70666-3
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