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For my exam time absence~.
(Photos, videos, concepts, or interesting problems are well appreciated)
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Formal definition.
Let \(\phi :[0,1]\to T\) (where \( T\) is a topological space) be a continous function (i.e. \(\phi ^{-1}\) of any open set \( O\) of \( T\) is an open set of the unit interval) from the unit interval to a topological space. Such map is said to be an space-filling curve if \(\phi\) is onto (i.e. if \phi passes through every element of \( T\) ).
Note
Generally, space filling curves are represented on spaces homeomorphic to \( E^{n}\) euclidian spaces. So to say, the plane, or any geometric solid, since these are the easiest ways to visualize a space filling curve. The most popular example, perhaps, is the two-dimensional Hilbert curve.
Images
A Hilbert curve from the unit interval to the unit cube
Peano Curve from the unit interval to the unit cube.
Flow Snake sapce filling curve.
Antithesis
Julia set. by page-avenue.
(Source: dvdp, via laconstante)
The Lorenz attractor
the Julia set.
Last three school weeks. Final projects, exams, and kind-of complicated topics.
When I end my Group Theory, advanced linear algebra courses and the overwhelming amounts of multivariable calc and mechanics I’ll be back. In the meantime, I’ll ony be posting pretty images.