Mandelbrot set (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Mandelbrot set" in English language version.

refsWebsite

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9doi.org

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5bu.edu

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allmusic.com

"Blue Man Group - Audio Album Reviews, Songs & More". Allmusic.com. Retrieved 4 July 2023.

ams.org

mathscinet.ams.org

Hubbard, J. H. (1993). "Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz" (PDF). Topological methods in modern mathematics (Stony Brook, NY, 1991). Houston, TX: Publish or Perish. pp. 467–511. MR 1215974.. Hubbard cites as his source a 1989 unpublished manuscript of Yoccoz.
Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267. arXiv:math.DS/9201282. doi:10.2307/121009. JSTOR 121009. MR 1626737. S2CID 14847943..

ams.org

Trout, Jody (April 2002). "Book Review: 'Flatterland: Like Flatland, Only More So" (PDF). Notices of the AMS. 49 (4): 462–465.

archive.org

Pountain, Dick (September 1986). "Turbocharging Mandelbrot". Byte. Retrieved 11 November 2015.

arxiv.org

Anna Miriam Benini (2017). "A survey on MLC, Rigidity and related topics". arXiv:1709.09869 [math.DS].
Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267. arXiv:math.DS/9201282. doi:10.2307/121009. JSTOR 121009. MR 1626737. S2CID 14847943..
Fang, Fang; Aschheim, Raymond; Irwin, Klee (December 2019). "The Unexpected Fractal Signatures in Fibonacci Chains". Fractal and Fractional. 3 (4): 49. arXiv:1609.01159. doi:10.3390/fractalfract3040049. ISSN 2504-3110.

books.google.com

The Mandelbrot set, theme and variations. Tan, Lei. Cambridge University Press, 2000. ISBN 978-0-521-77476-5. Section 2.1, "Yoccoz para-puzzles", p. 121
J. Milnor (1989). "Self-Similarity and Hairiness in the Mandelbrot Set". In M. C. Tangora (ed.). Computers in Geometry and Topology. New York: Taylor & Francis. pp. 211–257. ISBN 9780824780319.)
Piers Anthony (1992). Fractal Mode. HarperCollins. ISBN 978-0-246-13902-3.
Arthur C. Clarke (29 September 2011). The Ghost From The Grand Banks. Orion. ISBN 978-0-575-12179-9.

bridgesmathart.org

archive.bridgesmathart.org

Barrallo, Javier (2010). "Expanding the Mandelbrot Set into Higher Dimensions" (PDF). BridgesMathArt. Retrieved 15 September 2021.

brown.edu

math.brown.edu

Kahn, Jeremy (8 August 2001). "The Mandelbrot Set is Connected: a Topological Proof" (PDF).

bu.edu

math.bu.edu

"Mandelbrot Set Explorer: Mathematical Glossary". Retrieved 7 October 2007.
Devaney, Robert L. (7 January 2019). "Illuminating the Mandelbrot set" (PDF).
Devaney, Robert L. (29 December 1997). "The Mandelbrot Set and the Farey Tree" (PDF).
"The Mandelbrot Set Explorer Welcome Page". math.bu.edu. Retrieved 17 February 2024.
"7 The Fibonacci Sequence". math.bu.edu. Retrieved 17 February 2024.

cornell.edu

math.cornell.edu

Hubbard, J. H. (1993). "Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz" (PDF). Topological methods in modern mathematics (Stony Brook, NY, 1991). Houston, TX: Publish or Perish. pp. 467–511. MR 1215974.. Hubbard cites as his source a 1989 unpublished manuscript of Yoccoz.

pi.math.cornell.edu

Douady, A.; Hubbard, J (1982). "Iteration des Polynomials Quadratiques Complexes" (PDF).

desmos.com

"fibomandel angle 0.51". Desmos. Retrieved 17 February 2024.

doi.org

Mandelbrot, Benoit (1980). "Fractal aspects of the iteration of $z\mapsto \lambda z(1-z)$ for complex $\lambda ,z$ ". Annals of the New York Academy of Sciences. 357 (1): 249–259. doi:10.1111/j.1749-6632.1980.tb29690.x. S2CID 85237669.
Rees, Mary (January 2016). "One hundred years of complex dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185). Bibcode:2016RSPSA.47250453R. doi:10.1098/rspa.2015.0453. PMC 4786033. PMID 26997888.
Lei (1990). "Similarity between the Mandelbrot set and Julia Sets". Communications in Mathematical Physics. 134 (3): 587–617. Bibcode:1990CMaPh.134..587L. doi:10.1007/bf02098448. S2CID 122439436.
Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267. arXiv:math.DS/9201282. doi:10.2307/121009. JSTOR 121009. MR 1626737. S2CID 14847943..
Katunin, Andrzej; Fedio, Kamil (2015). "On a Visualization of the Convergence of the Boundary of Generalized Mandelbrot Set to (n-1)-Sphere" (PDF). Journal of Applied Mathematics and Computational Mechanics. 14 (1): 63–69. doi:10.17512/jamcm.2015.1.06. Retrieved 18 May 2022.
Klebanoff, Aaron D. (2001). "π in the Mandelbrot Set". Fractals. 9 (4): 393–402. doi:10.1142/S0218348X01000828.
Devaney, Robert L. (April 1999). "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence". The American Mathematical Monthly. 106 (4): 289–302. doi:10.2307/2589552. ISSN 0002-9890. JSTOR 2589552.
Fang, Fang; Aschheim, Raymond; Irwin, Klee (December 2019). "The Unexpected Fractal Signatures in Fibonacci Chains". Fractal and Fractional. 3 (4): 49. arXiv:1609.01159. doi:10.3390/fractalfract3040049. ISSN 2504-3110.

dx.doi.org

Devaney, Robert L. (April 1999). "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence". The American Mathematical Monthly. 106 (4): 289–302. doi:10.2307/2589552. ISSN 0002-9890. JSTOR 2589552.

ghostarchive.org

"Number Sequences in the Mandelbrot Set". youtube.com. The Mathemagicians' Guild. 4 June 2020. Archived from the original on 30 October 2021.

gizmodo.com

Mandelbaum, Ryan F. (2018). "This Trippy Music Video Is Made of 3D Fractals." Retrieved 17 January 2019

harvard.edu

ui.adsabs.harvard.edu

Rees, Mary (January 2016). "One hundred years of complex dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185). Bibcode:2016RSPSA.47250453R. doi:10.1098/rspa.2015.0453. PMC 4786033. PMID 26997888.
Lei (1990). "Similarity between the Mandelbrot set and Julia Sets". Communications in Mathematical Physics. 134 (3): 587–617. Bibcode:1990CMaPh.134..587L. doi:10.1007/bf02098448. S2CID 122439436.

abel.math.harvard.edu

Robert Brooks and Peter Matelski, The dynamics of 2-generator subgroups of PSL(2,C), in Irwin Kra (1 May 1981). Irwin Kra (ed.). Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (PDF). Bernard Maskit. Princeton University Press. ISBN 0-691-08267-7. Archived from the original (PDF) on 28 July 2019. Retrieved 1 July 2019.

icollector.com

"Hannah Marks "Amanda Brotzman" customized black leather jacket from Dirk Gently's Holistic Detective Agency". www.icollector.com.

jonathancoulton.com

"Mandelbrot Set". JoCopeda. Retrieved 15 January 2015.

jstor.org

"Exploring The Mandelbrot Set". Scientific American. 253 (2): 4. August 1985. JSTOR 24967754 – via JSTOR.
Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267. arXiv:math.DS/9201282. doi:10.2307/121009. JSTOR 121009. MR 1626737. S2CID 14847943..
Devaney, Robert L. (April 1999). "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence". The American Mathematical Monthly. 106 (4): 289–302. doi:10.2307/2589552. ISSN 0002-9890. JSTOR 2589552.

lexico.com

"Mandelbrot set". Lexico UK English Dictionary. Oxford University Press. Archived from the original on 31 January 2022.

merriam-webster.com

"Mandelbrot set". Merriam-Webster.com Dictionary. Retrieved 30 January 2022.

mrob.com

"Escape Radius". Retrieved 17 January 2024.

nbn-resolving.de

Jung, Wolf (2002). Homeomorphisms on Edges of the Mandelbrot Set (Doctoral thesis). RWTH Aachen University. urn:nbn:de:hbz:82-opus-3719.

nih.gov

pubmed.ncbi.nlm.nih.gov

R.P. Taylor & J.C. Sprott (2008). "Biophilic Fractals and the Visual Journey of Organic Screen-savers" (PDF). Nonlinear Dynamics, Psychology, and Life Sciences. 12 (1). Society for Chaos Theory in Psychology & Life Sciences: 117–129. PMID 18157930. Retrieved 1 January 2009.
Rees, Mary (January 2016). "One hundred years of complex dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185). Bibcode:2016RSPSA.47250453R. doi:10.1098/rspa.2015.0453. PMC 4786033. PMID 26997888.

ncbi.nlm.nih.gov

Rees, Mary (January 2016). "One hundred years of complex dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185). Bibcode:2016RSPSA.47250453R. doi:10.1098/rspa.2015.0453. PMC 4786033. PMID 26997888.

patreon.com

"Maths Town". Patreon. Retrieved 17 February 2024.

pcss.pl

reader.digitarium.pcss.pl

Katunin, Andrzej; Fedio, Kamil (2015). "On a Visualization of the Convergence of the Boundary of Generalized Mandelbrot Set to (n-1)-Sphere" (PDF). Journal of Applied Mathematics and Computational Mechanics. 14 (1): 63–69. doi:10.17512/jamcm.2015.1.06. Retrieved 18 May 2022.

projecteuclid.org

Lei (1990). "Similarity between the Mandelbrot set and Julia Sets". Communications in Mathematical Physics. 134 (3): 587–617. Bibcode:1990CMaPh.134..587L. doi:10.1007/bf02098448. S2CID 122439436.

semanticscholar.org

api.semanticscholar.org

Mandelbrot, Benoit (1980). "Fractal aspects of the iteration of $z\mapsto \lambda z(1-z)$ for complex $\lambda ,z$ ". Annals of the New York Academy of Sciences. 357 (1): 249–259. doi:10.1111/j.1749-6632.1980.tb29690.x. S2CID 85237669.
Lei (1990). "Similarity between the Mandelbrot set and Julia Sets". Communications in Mathematical Physics. 134 (3): 587–617. Bibcode:1990CMaPh.134..587L. doi:10.1007/bf02098448. S2CID 122439436.
Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267. arXiv:math.DS/9201282. doi:10.2307/121009. JSTOR 121009. MR 1626737. S2CID 14847943..

sjsu.edu

cs.sjsu.edu

Rudy Rucker's discussion of the CCM: CS.sjsu.edu

thatsmaths.com

thatsmaths (7 December 2023). "The Logistic Map is hiding in the Mandelbrot Set". ThatsMaths. Retrieved 18 February 2024.

thewest.com.au

Moeller, Olga de. (2018)."what are Fractals?" Retrieved 17 January 2019.

tor.com

"The Great Alan Moore Reread: Big Numbers by Tim Callahan". Tor.com. 21 May 2012.

upi.com

Sheridan, Wade (20 November 2020). "Google honors mathematician Benoit Mandelbrot with new Doodle". United Press International. Retrieved 30 December 2020.

washington.edu

sites.math.washington.edu

Allaway, Emily (May 2016). "The Mandelbrot Set and the Farey Tree" (PDF).

web.archive.org

"Mandelbrot set". Lexico UK English Dictionary. Oxford University Press. Archived from the original on 31 January 2022.
Robert Brooks and Peter Matelski, The dynamics of 2-generator subgroups of PSL(2,C), in Irwin Kra (1 May 1981). Irwin Kra (ed.). Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (PDF). Bernard Maskit. Princeton University Press. ISBN 0-691-08267-7. Archived from the original (PDF) on 28 July 2019. Retrieved 1 July 2019.

wisc.edu

sprott.physics.wisc.edu

R.P. Taylor & J.C. Sprott (2008). "Biophilic Fractals and the Visual Journey of Organic Screen-savers" (PDF). Nonlinear Dynamics, Psychology, and Life Sciences. 12 (1). Society for Chaos Theory in Psychology & Life Sciences: 117–129. PMID 18157930. Retrieved 1 January 2009.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Mandelbrot Set". mathworld.wolfram.com. Retrieved 24 January 2024.
Weisstein, Eric W. "Mandelbrot Set Lemniscate". Wolfram Mathworld. Retrieved 17 July 2023.

worldcat.org

Devaney, Robert L. (April 1999). "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence". The American Mathematical Monthly. 106 (4): 289–302. doi:10.2307/2589552. ISSN 0002-9890. JSTOR 2589552.
Fang, Fang; Aschheim, Raymond; Irwin, Klee (December 2019). "The Unexpected Fractal Signatures in Fibonacci Chains". Fractal and Fractional. 3 (4): 49. arXiv:1609.01159. doi:10.3390/fractalfract3040049. ISSN 2504-3110.

youtube.com

"Number Sequences in the Mandelbrot Set". youtube.com. The Mathemagicians' Guild. 4 June 2020. Archived from the original on 30 October 2021.