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© V BORRELLI / R DENIS / F LAZARUS / B THIBERT / M THEILLIERE / ICJ / G-SCOP / LJK / uni. Luxembourg, soutenu par le FNR / CNRS



Infinity always finds a way

Close-up view of a surface representing hyperbolic space and its boundary at infinity. The existence of such a surface was predicted by the mathematician John Nash in the 1950s. It has now actually been constructed, with the help of computers, by a team of scientists, who are attempting to visualise paradoxical mathematical objects. This surface, resulting from an infinite entanglement of corrugations (or folds), has an astonishing property: the shortest path between a point on its sinuous edge and any other point on this surface is infinitely long. Visualisations of this kind make it possible to explore a new geometry, half-way between that of fractals and that of ordinary surfaces: the geometry of smooth fractals. This image is one of the winners of the 2022 La preuve par l’image (LPPI) photography competition.

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