Mandelbrot set (English Wikipedia)

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 Hubbard cites as his source a 1989 unpublished manuscript of Yoccoz.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

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Tiozzo, Giulio (15 May 2013), Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set, arXiv:1305.3542
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Brockmoeller, Thies; Scherz, Oscar; Srkalovic, Nedim (2025). "Pi in the Mandelbrot set everywhere". arXiv:2505.07138 [math.DS].
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.
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Gauthier, Thomas; Vigny, Gabriel (2 February 2016), Distribution of postcritically finite polynomials iii: Combinatorial continuity, arXiv:1602.00925

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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.
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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.
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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.)
Andrzej Katunin (2017). A Concise Introduction to Hypercomplex Fractals. CRC Press. p. 21. ISBN 978-1-351-80121-8.
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.
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Crownover, Richard M. (1995). Introduction to Fractals and Chaos. Jones and Bartlett. p. 201. ISBN 978-0-86720-464-3.
Arthur C. Clarke (2011). The Ghost From The Grand Banks. Orion. ISBN 978-0-575-12179-9.
Piers Anthony (1992). Fractal Mode. HarperCollins. ISBN 978-0-246-13902-3.

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

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

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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).

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

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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.

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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.

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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.

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

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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.

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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 (Global: 3,707^th place; English: 2,409^th place)

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 (Global: low place; English: low place)

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 (Global: 149^th place; English: 178^th place)

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.

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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..

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"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.
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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.

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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.

x.com (Global: low place; English: low place)

Cicierega, Neil [@neilcic] (17 April 2016). ""It's Gonna Get Weird", the final unused song I wrote for Gravity Falls. http://neilblr.com/post/142982667678" (Tweet). Archived from the original on 9 April 2022. Retrieved 30 August 2025 – via Twitter.

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Mandelbrot set (English Wikipedia)

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ncbi.nlm.nih.gov

patreon.com (Global: 8,774th place; English: 5,439th place)

pcss.pl (Global: low place; English: low place)

reader.digitarium.pcss.pl

projecteuclid.org (Global: 3,707th place; English: 2,409th place)

rgdoi.net (Global: low place; English: low place)

sciencedirect.com (Global: 149th place; English: 178th place)

semanticscholar.org (Global: 11th place; English: 8th place)

api.semanticscholar.org

sjsu.edu (Global: 6,511th place; English: 4,308th place)

cs.sjsu.edu

thatsmaths.com (Global: low place; English: low place)

thewest.com.au (Global: 3,165th place; English: 1,780th place)

tor.com (Global: 1,483rd place; English: 828th place)

upi.com (Global: 290th place; English: 202nd place)

utah.edu (Global: 2,446th place; English: 1,661st place)

cometcloud.sci.utah.edu

washington.edu (Global: 1,067th place; English: 749th place)

sites.math.washington.edu

web.archive.org (Global: 1st place; English: 1st place)

wisc.edu (Global: 1,045th place; English: 746th place)

sprott.physics.wisc.edu

wolfram.com (Global: 513th place; English: 537th place)

mathworld.wolfram.com

worldcat.org (Global: 5th place; English: 5th place)

search.worldcat.org

x.com (Global: low place; English: low place)

youtube.com (Global: 9th place; English: 13th place)

allmusic.com (Global: 25^th place; English: 22^nd place)

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

brown.edu (Global: 2,481^st place; English: 1,558^th place)

bu.edu (Global: 2,120^th place; English: 1,328^th place)

buffalo.edu (Global: 4,241^st place; English: 2,850^th place)

cornell.edu (Global: 332^nd place; English: 246^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

genius.com (Global: 955^th place; English: 729^th place)

ghostarchive.org (Global: 32^nd place; English: 21^st place)

gizmodo.com (Global: 474^th place; English: 329^th place)

harvard.edu (Global: 18^th place; English: 17^th place)

jstor.org (Global: 26^th place; English: 20^th place)

lexico.com (Global: 1,242^nd place; English: 853^rd place)

merriam-webster.com (Global: 209^th place; English: 191^st place)

nbn-resolving.de (Global: 3,251^st place; English: 7,630^th place)

nih.gov (Global: 4^th place; English: 4^th place)

patreon.com (Global: 8,774^th place; English: 5,439^th place)

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

sciencedirect.com (Global: 149^th place; English: 178^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

sjsu.edu (Global: 6,511^th place; English: 4,308^th place)

thewest.com.au (Global: 3,165^th place; English: 1,780^th place)

tor.com (Global: 1,483^rd place; English: 828^th place)

upi.com (Global: 290^th place; English: 202^nd place)

utah.edu (Global: 2,446^th place; English: 1,661^st place)

washington.edu (Global: 1,067^th place; English: 749^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

wisc.edu (Global: 1,045^th place; English: 746^th place)

wolfram.com (Global: 513^th place; English: 537^th place)

worldcat.org (Global: 5^th place; English: 5^th place)

youtube.com (Global: 9^th place; English: 13^th place)