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Mondrian was one of the most significant painters of the 20th century. He wasa prominent member of DeStijl, the movement which revolutionized art by settingit free of the obligation to make images of existing objects, persons, orsituations. DeStijl was one of the interrelated movements in early 20th centuryEurope including Cubism, Constructivism, the Futurists, and Dada. Theirdisruptive ideas changed the meaning of Western art. It was Mondrian, more thananyone else, who worked restlessly to find expression for the purest possiblekind of beauty and truth, based on a theory called Neoplasticism. He wasalready famous during his lifetime and still now, his name is almost synonymfor modern art. We analyze the structure of the system of black lines in hispaintings and put the hypothesis to the test that the paintings could beobtained by recursive (binary) splitting. We used a novel tailor-madeinteractive analysis tool and apply it to as many Mondrian paintings aspossible (in total 147). The results will be explained in a visual manner, butwe also present statistical findings from the analysis of the 147 paintings.Our main conclusion is that the hypothesis of splitting decomposition is ingeneral not true. It is possible to make Mondrian-like compositions bysplitting, yet one misses out on a great deal of Neoplastic beauty if one wouldwork by splitting only. It is possible to consider all crossings as pairs ofTees, but that is clumsy, and it leaves out essential information. Moreoverthere are other important design decisions of Mondrian, such as thekeeping-distance to the canvas-edge which are not well-described by splitting.

Analyzing the Structure of Mondrian's 1920-1940 Compositions