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Illustrate graphically how a diffeomorphism distorts a rubick's cube - no text, no math, just the cube in original form (left) and distorted form (right), hand drawing in pencil with vivid colors, dark background
A diffeomorphism is a bijective mapping between two smooth manifolds that is smooth in both directions. More precisely, a mapping from one smooth manifold to another is a diffeomorphism if it satisfies all three conditions: (1) bijectivity: the mapping is one-to-one and onto, i.e. very point of the first manifold corresponds to exactly one point of the second, and vice versa; (2) smoothness: the mapping is infinitely differentiable, i.e. derivatives of all orders exist and are continuous when expressed in smooth local coordinates; (3) smooth inverse: the inverse mapping is also infinitely differentiable. Two smooth manifolds are said to be diffeomorphic if there exists a diffeomorphism between them. Intuitively, a diffeomorphism is a smooth, reversible deformation that preserves the differentiable structure, without tearing, gluing, or introducing singularities.
