creator: Alberto Sevoso This really happens, all the time: Diffusion 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 topology — knotting within themselves or linking with other hoops of different colour. Those are some nice 3-manifolds. via chels(Source: behance.net)
![\frac{\partial\phi(\mathbf{r},t)}{\partial t} = \nabla \cdot \big[ D(\phi,\mathbf{r}) \, \nabla\phi(\mathbf{r},t) \big],](http://upload.wikimedia.org/wikipedia/en/math/9/c/5/9c5f4d7f64c748e1eb4ff47bf31bb390.png)
![\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]](http://upload.wikimedia.org/wikipedia/en/math/c/c/2/cc2d8bf88c0d0cae69670fbba15634f3.png)
![\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]](http://upload.wikimedia.org/wikipedia/en/math/8/a/6/8a605287536e8843d4d94ec8fc3eb6b3.png)
