In a painting called 'Catastrophe Theory' from 1983, the German painter Sigmar Polke included the math diagrams shown in the linked image below (for another image see here: https://www.sfmoma.org/artwork/2010.261/).

I'm trying to trace the source of the diagrams, i.e. the publication they were taken from.

Can anybody help me out? Even a suggestion about what they show would be helpful.
My guess is that they have to do with chaos theory or with fractals, but I really have no idea.


[Series of math diagrams, possibly of fractals]

  • 5
    $\begingroup$ Looks like phase potraits $\endgroup$ Dec 10, 2023 at 5:02

1 Answer 1


Direct Connection is with 'Catastrophe Theory'

Classic text is "Catastrophe Theory" [ "Vladimir Igorevich Arnold" ]

Images OP wants are available at Page 25 :

P 25

Page 14 :

P 14

Page 24 :

P 24

Details about the Domain :
https://pure.iiasa.ac.at/id/eprint/8095/1/RP-06-007.pdf https://mathworld.wolfram.com/CatastropheTheory.html

  • 1
    $\begingroup$ Nice! The two artists were nearly of the same age and sadly died only one week apart: V.I. Arnold 3-June-2010 and S. Polke 10-June-2010. Before someone remarks that Arnold was a mathematican. Yes but he was definitely an artist as well. $\endgroup$
    – Kurt G.
    Dec 10, 2023 at 9:16
  • $\begingroup$ In a way , it seems that Arnold was some "Strange Attractor" in at least two senses , where Polke was concerned !! $\endgroup$
    – Prem
    Dec 10, 2023 at 9:24
  • $\begingroup$ I am a big admirer of him. Any chance we could find out if they knew each other personally? Also the question arises if Arnold used art of Polke somewhere. $\endgroup$
    – Kurt G.
    Dec 10, 2023 at 9:26
  • $\begingroup$ Plagiarism accusations might arise when Polke uses the Images made by Arnold. To avoid that , I am certain Polke informed Arnold about the usage , @KurtG. , which would imply that Polke met Arnold , at least via telephone or email or mail , to get Permission. I see other indications of interactions , though no confirmatory evidences ! $\endgroup$
    – Prem
    Dec 10, 2023 at 12:39
  • $\begingroup$ Thanks Prem! Great to have this mystery resolved. I can't confirm that Polke and Arnold met, but as far as copyright goes, Polke just harvested things at will. He never asked permission. Until recently that was standard in the art world. Then some big law suits came along :-) $\endgroup$ Dec 11, 2023 at 6:42

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