Analysing Chess

Some deepening on the chaos concept by Klee

 By Roberto Giunti







With the present paper I will present some consideration about the way the Swiss painter Paul Klee (1879-1940) conceived the idea of chaos. I have elsewhere already discussed the subject in some detail. The present article is intended to furnish further deepening about it, by analysing Klee’s painting Chess (1931).

In short, the thesis I assert is that according to Klee’s way of thinking the idea of chaos is both theoretically and practically quite close to the concept of deterministic chaos, as currently seen by sciences, i.e. an unpredictable dynamic behaviour of systems subjected to simple, deterministic, iterative rules. Particularly, I will suggest that often Klee builds structures by means of iterative rules, which are pushed to assume highly irregular behaviours, in order to produce ever new and unexpected outcomes, and Chess is a remarkable example of it. This holds deep and meaningful connections with one of the most important concepts in complexity sciences, expressed by the popular but effective slogan: "complexity at the edge of chaos"





Three key features in Klee’s thought

Deterministic chaos

Recalling some results already presented


The perspective of the coloured bars

The perspective of the background

A parenthetic note on non-linearity

Returning to Chess

Putting things together


Acknowledgements, References and Notes


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