http://de.evo-art.org/index.php?action=history&feed=atom&title=Inversive_Diversions_and_Diversive_Inversions 2026-05-04T12:20:01Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Inversive_Diversions_and_Diversive_Inversions&diff=33272&oldid=prev 2017-12-07T10:06:39Z

<p>Die Seite wurde neu angelegt: „ == Referenz == Gregg Helt: <a href="/index.php?title=Inversive_Diversions_and_Diversive_Inversions" title="Inversive Diversions and Diversive Inversions">Inversive Diversions and Diversive Inversions</a>. In: <a href="/index.php?title=Bridges_2017" title="Bridges 2017">Bridges 2017</a>, Pages 467–470. == DOI == == Abstract == In this pape…“</p> <p><b>Neue Seite</b></p><div><br /> == Referenz == <br /> Gregg Helt: [[Inversive Diversions and Diversive Inversions]]. In: [[Bridges 2017]], Pages 467–470. <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> In this paper, we first briefly review aspects of inversive geometry and inversive fractals. Motivated by a desire to expand our geometric and artistic toolkit, we then introduce mixed-restriction limit sets as a new technique for use with iterated function systems and groups of circle inversions to create previously undiscovered 2D inversive fractals. We also apply this technique to diverse shape-based inversions that are closely related to circle inversion. Finally, we explore extending mixed-restriction limit sets and shape-based inversions into 3D to generate 3D inversive fractals. <br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> @inproceedings{bridges2017:467,<br /> author = {Gregg Helt},<br /> title = {Inversive Diversions and Diversive Inversions},<br /> pages = {467--470},<br /> booktitle = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},<br /> year = {2017},<br /> editor = {David Swart, Carlo H. S\&#039;equin, and Krist\&#039;of Fenyvesi},<br /> isbn = {978-1-938664-22-9},<br /> issn = {1099-6702},<br /> publisher = {Tessellations Publishing},<br /> address = {Phoenix, Arizona},<br /> note = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-467.pdf}}<br /> }<br /> <br /> == Used References == <br /> [1] M. F. Barnsley and S. Demko, “Iterated Function Systems and the Global Construction of Fractals”,<br /> Proceedings of the Royal Society of London, vol. 399, no. 1817, pp. 243–275, 1985<br /> <br /> [2] B. B. Mandelbrot, “Self-inverse Fractals, Apollonian Nets, and Soap”, The Fractal Geometry of<br /> Nature, Chapter 18, pp. 166-179, 1982<br /> <br /> [3] V. Bulatov, “Inversive Kaleidoscopes and Their Visualization”, Proceedings of Bridges 2014:<br /> Mathematics, Music, Art, Architecture, Culture, pp. 329–332, 2014<br /> <br /> [4] R. M. Baram and H. J. Herrmann, “Self-similar Space-filling Packings in Three Dimensions”,<br /> Fractals, vol. 12, no. 03, pp. 293–301, 2004<br /> <br /> [5] C. Clancy and M. Frame, “Fractal Geometry of Restricted Sets of Circle Inversions”, Fractals, vol.<br /> 03, no. 04, pp. 689–699, 1995<br /> <br /> [6] K. Gdawiec, “Star-shaped Set Inversion Fractals”, Fractals, vol. 22, no. 04, pp. 1450009.1-7, 2014<br /> <br /> [7] J. L. Ramírez and G. N. Rubiano, “A Generalization of the Spherical Inversion”, International<br /> Journal of Mathematical Education in Science and Technology, vol. 48, no. 1, pp. 132–149, 2017<br /> <br /> [8] J. Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract<br /> shapes”, American Journal of Botany, vol. 90, no. 3, pp. 333–338, 2003<br /> <br /> [9] G. Helt, “A Rose By Any Other Name...”, Proceedings of Bridges 2016: Mathematics, Music, Art,<br /> Architecture, Education, Culture, pp. 445–448, 2016<br /> <br /> [10] A. Maschke, JWildfire software, 2011. Current release v3.10 (April 2017), http://jwildfire.org<br /> <br /> <br /> == Links == <br /> <br /> === Full Text === <br /> http://archive.bridgesmathart.org/2017/bridges2017-467.pdf<br /> <br /> [[internal file]] <br /> <br /> <br /> === Sonstige Links ===</div>

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