Mandelbrot set (English Wikipedia)

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

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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 Hubbard cites as his source a 1989 unpublished manuscript of Yoccoz.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

Tiozzo, Giulio (15 May 2013), Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set, arXiv:1305.3542
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..
https://arxiv.org/abs/2505.07138
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.
Inou, Hiroyuki; Kawahira, Tomoki (23 March 2022), Accessible hyperbolic components in anti-holomorphic dynamics, arXiv:2203.12156
Gauthier, Thomas; Vigny, Gabriel (2 February 2016), Distribution of postcritically finite polynomials iii: Combinatorial continuity, arXiv:1602.00925

books.google.com

Cooper, S. B.; Löwe, Benedikt; Sorbi, Andrea (28 November 2007). New Computational Paradigms: Changing Conceptions of What is Computable. Springer Science & Business Media. p. 450. ISBN 978-0-387-68546-5.
Nakos, George (20 May 2024). Elementary Linear Algebra with Applications: MATLAB®, Mathematica® and MaplesoftTM. Walter de Gruyter GmbH & Co KG. p. 322. ISBN 978-3-11-133185-0.
Addison, Paul S. (1 January 1997). Fractals and Chaos: An illustrated course. CRC Press. p. 110. ISBN 978-0-8493-8443-1.
Briggs, John (1992). Fractals: The Patterns of Chaos : a New Aesthetic of Art, Science, and Nature. Simon and Schuster. p. 77. ISBN 978-0-671-74217-1.
Hewson, Stephen Fletcher (2009). A Mathematical Bridge: An Intuitive Journey in Higher Mathematics. World Scientific. p. 155. ISBN 978-981-283-407-2.
Peitgen, Heinz-Otto; Richter, Peter H. (1 December 2013). The Beauty of Fractals: Images of Complex Dynamical Systems. Springer Science & Business Media. p. 166. ISBN 978-3-642-61717-1. the Mandelbrot set is very diverse in its different regions
Hunt, John (1 October 2023). Advanced Guide to Python 3 Programming. Springer Nature. p. 117. ISBN 978-3-031-40336-1.
Oberguggenberger, Michael; Ostermann, Alexander (24 October 2018). Analysis for Computer Scientists: Foundations, Methods, and Algorithms. Springer. p. 131. ISBN 978-3-319-91155-7.
Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar (6 December 2012). Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set. Springer Science & Business Media. p. 415. ISBN 978-1-4612-4406-6.
Gulick, Denny; Ford, Jeff (10 May 2024). Encounters with Chaos and Fractals. CRC Press. pp. §7.2. ISBN 978-1-003-83578-3.
Bialynicki-Birula, Iwo; Bialynicka-Birula, Iwona (21 October 2004). Modeling Reality: How Computers Mirror Life. OUP Oxford. p. 80. ISBN 978-0-19-853100-5.
Schleicher, Dierk (3 November 2009). Complex Dynamics: Families and Friends. CRC Press. pp. xii. ISBN 978-1-4398-6542-2.
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
Brucks, Karen M.; Bruin, Henk (28 June 2004). Topics from One-Dimensional Dynamics. Cambridge University Press. p. 264. ISBN 978-0-521-54766-6.
Devaney, Robert (9 March 2018). An Introduction To Chaotic Dynamical Systems. CRC Press. p. 147. ISBN 978-0-429-97085-6.
Ivancevic, Vladimir G.; Ivancevic, Tijana T. (6 February 2007). High-Dimensional Chaotic and Attractor Systems: A Comprehensive Introduction. Springer Science & Business Media. pp. 492–493. ISBN 978-1-4020-5456-3.
Devaney, Robert L.; Branner, Bodil (1994). Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets: The Mathematics Behind the Mandelbrot and Julia Sets. American Mathematical Soc. pp. 18–19. ISBN 978-0-8218-0290-8.
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.)
Lisle, Jason (1 July 2021). Fractals: The Secret Code of Creation. New Leaf Publishing Group. p. 28. ISBN 978-1-61458-780-4.
Devaney, Robert L. (4 May 2018). A First Course In Chaotic Dynamical Systems: Theory And Experiment. CRC Press. p. 259. ISBN 978-0-429-97203-4.
Kappraff, Jay (2002). Beyond Measure: A Guided Tour Through Nature, Myth, and Number. World Scientific. p. 437. ISBN 978-981-02-4702-7.
Schleicher, Dierk (2004). "On Fibers and Local Connectivity of Mandelbrot and Multibrot Sets". In Lapidus, Michel L.; van Frankenhuijsen, Machiel (eds.). Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot, Part 1. American Mathematical Society. pp. 477–517.
Jarzębowicz, Aleksander; Luković, Ivan; Przybyłek, Adam; Staroń, Mirosław; Ahmad, Muhammad Ovais; Ochodek, Mirosław (2 January 2024). Software, System, and Service Engineering: S3E 2023 Topical Area, 24th Conference on Practical Aspects of and Solutions for Software Engineering, KKIO 2023, and 8th Workshop on Advances in Programming Languages, WAPL 2023, Held as Part of FedCSIS 2023, Warsaw, Poland, 17–20 September 2023, Revised Selected Papers. Springer Nature. p. 142. ISBN 978-3-031-51075-5.
Katunin, Andrzej (5 October 2017). A Concise Introduction to Hypercomplex Fractals. CRC Press. p. 6. ISBN 978-1-351-80121-8.
Farlow, Stanley J. (23 October 2012). An Introduction to Differential Equations and Their Applications. Courier Corporation. p. 447. ISBN 978-0-486-13513-7.
Saha, Amit (1 August 2015). Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!. No Starch Press. p. 176. ISBN 978-1-59327-640-9.
Crownover, Richard M. (1995). Introduction to Fractals and Chaos. Jones and Bartlett. p. 201. ISBN 978-0-86720-464-3.
Piers Anthony (1992). Fractal Mode. HarperCollins. ISBN 978-0-246-13902-3.
Arthur C. Clarke (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.

buffalo.edu

acsu.buffalo.edu

Cunningham, Adam (20 December 2013). "Displaying the Internal Structure of the Mandelbrot Set" (PDF).

complex-analysis.com

Campuzano, Juan Carlos Ponce (20 November 2020). "Complex Analysis". Complex Analysis — The Mandelbrot Set. Archived from the original on 16 October 2024. Retrieved 5 March 2025.

cornell.edu

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

csusb.edu

scholarworks.lib.csusb.edu

Redona, Jeffrey Francis (1996). The Mandelbrot set (Masters of Arts in Mathematics). Theses Digitization Project.

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.
Hooper, Kenneth J. (1 January 1991). "A note on some internal structures of the Mandelbrot Set". Computers & Graphics. 15 (2): 295–297. doi:10.1016/0097-8493(91)90082-S. ISSN 0097-8493.
Youvan, Douglas C (2024). "Shades Within: Exploring the Mandelbrot Set Through Grayscale Variations". Pre-print. doi:10.13140/RG.2.2.24445.74727.

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.

geeksforgeeks.org

"Mandelbrot Fractal Set visualization in Python". GeeksforGeeks. 3 October 2018. Retrieved 23 March 2025.

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 (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.

hws.edu

math.hws.edu

"Mandelbrot Viewer". math.hws.edu. Retrieved 1 March 2025.

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.
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.

karlsims.com

Sims, Karl. "Understanding Julia and Mandelbrot Sets". karlsims.com. Retrieved 27 January 2025.

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. Merriam-Webster. 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.

rgdoi.net

Youvan, Douglas C (2024). "Shades Within: Exploring the Mandelbrot Set Through Grayscale Variations". Pre-print. doi:10.13140/RG.2.2.24445.74727.

sciencedirect.com

Hooper, Kenneth J. (1 January 1991). "A note on some internal structures of the Mandelbrot Set". Computers & Graphics. 15 (2): 295–297. doi:10.1016/0097-8493(91)90082-S. ISSN 0097-8493.

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.

utah.edu

cometcloud.sci.utah.edu

"Mandelbrot Set". cometcloud.sci.utah.edu. Retrieved 22 March 2025.

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 (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.
Campuzano, Juan Carlos Ponce (20 November 2020). "Complex Analysis". Complex Analysis — The Mandelbrot Set. Archived from the original on 16 October 2024. Retrieved 5 March 2025.

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

search.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.
Hooper, Kenneth J. (1 January 1991). "A note on some internal structures of the Mandelbrot Set". Computers & Graphics. 15 (2): 295–297. doi:10.1016/0097-8493(91)90082-S. ISSN 0097-8493.

youtube.com

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