creator: Alberto Sevoso

  • This really happens, all the time:
  • Diffusion
    frac{partialphi(mathbf{r},t)}{partial t} = nabla cdot big[ D(phi,mathbf{r}) , nablaphi(mathbf{r},t) big],
    frac{partialphi(mathbf{r},t)}{partial t} = sum_{i=1}^3sum_{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{partialphi(mathbf{r},t)}{partial t} = nablacdot left[D(phi,mathbf{r})right] nabla phi(mathbf{r},t) + {rm tr} Big[ D(phi,mathbf{r})big(nablanabla^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


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