creator: Alberto Sevoso

  • This really happens, all the time:
  • Diffusion
    \frac{\partial\phi(\mathbf{r},t)}{\partial t} = \nabla \cdot \big[ D(\phi,\mathbf{r}) \, \nabla\phi(\mathbf{r},t) \big],
    \frac{\partial\phi(\mathbf{r},t)}{\partial t} = \sum_{i=1}^3\sum_{j=1}^3 \frac{\partial}{\partial x_i}\left[D_{ij}(\phi,\mathbf{r})\frac{\partial \phi(\mathbf{r},t)}{\partial x_j}\right]
    \frac{\partial\phi(\mathbf{r},t)}{\partial t} = \nabla\cdot \left[D(\phi,\mathbf{r})\right] \nabla \phi(\mathbf{r},t) + {\rm tr} \Big[ D(\phi,\mathbf{r})\big(\nabla\nabla^T \phi(\mathbf{r},t)\big)\Big]
  • Schooly mathematics is all about rigid, blocky shapes. But since people realised that the infinite limit of a curve is straight, that dynamics are just another dimension (time), then all tame ploop-ploppulous and fandangulous shapes become fair game.
  • "Later" mathematics takes those simple forms—triangles, squares, circles—to the limit and comes up with these kinds of shapes.
  • A few of them have non-trivial topologyknotting within themselves or linking with other hoops of different colour.
  • Those are some nice 3-manifolds.

via chels

(Source: behance.net)







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