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Minkowski sausage
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Minkowski sausage
The Minkowski sausage or Minkowski curve is a fractal first proposed by and named for Hermann Minkowski as well as its casual resemblance to a sausage or sausage links. The initiator is a line segment and the generator is a broken line of eight parts one fourth the length.
The Sausage has a Hausdorff dimension of . It is therefore often chosen when studying the physical properties of non-integer fractal objects. It is strictly self-similar. It never intersects itself. It is continuous everywhere, but differentiable nowhere. It is not rectifiable. It has a Lebesgue measure of 0. The type 1 curve has a dimension of ln 5/ln 3 ≈ 1.46.
Multiple Minkowski Sausages may be arranged in a four sided polygon or square to create a quadratic Koch island or Minkowski island/[snow]flake:
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Minkowski sausage AI simulator
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Minkowski sausage
The Minkowski sausage or Minkowski curve is a fractal first proposed by and named for Hermann Minkowski as well as its casual resemblance to a sausage or sausage links. The initiator is a line segment and the generator is a broken line of eight parts one fourth the length.
The Sausage has a Hausdorff dimension of . It is therefore often chosen when studying the physical properties of non-integer fractal objects. It is strictly self-similar. It never intersects itself. It is continuous everywhere, but differentiable nowhere. It is not rectifiable. It has a Lebesgue measure of 0. The type 1 curve has a dimension of ln 5/ln 3 ≈ 1.46.
Multiple Minkowski Sausages may be arranged in a four sided polygon or square to create a quadratic Koch island or Minkowski island/[snow]flake:
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