Colophon

The folds (gyri and sulci) are a labyrinthine Turing pattern, a solution of the Swift–Hohenberg equation

introduced by Jack Swift and Pierre Hohenberg in 1977 to describe convection rolls [1], and now a standard model of pattern formation. For the uniform state is unstable to perturbations with wavenumber close to , and stripes of wavelength emerge.

The logo uses and a wavelength of 0.19 (in units where the hemisphere is about 2.3 long). Starting from random noise on a 640 × 480 grid, the equation is integrated for 170 time steps of size 0.5 with a semi-implicit Fourier spectral scheme: the linear operator is treated implicitly in Fourier space and the cubic term explicitly. In the last 60 steps the solution is pinned to a negative value just outside the brain, which rounds off the folds at the edge of the cortex.

The fibres are three level sets of the solution, , and , so each fold is drawn as a bundle of nested curves.

Each short piece of fibre is coloured by its direction, borrowing the idea of the colour code of diffusion tensor imaging (DTI), which maps the orientation of white-matter tracts in the living brain [2]: one colour for front-to-back fibres, one for top-to-bottom, and two for the oblique directions. In the logo the four directions take colours from the Nord palette (below).

The outline of the hemisphere, its contour seen from the side, is a smooth closed curve (a Catmull–Rom spline [3]) through 22 points traced from a lateral view of a real left hemisphere. From it the program computes, for every point of the picture, its distance to the contour, counted negative inside the brain and positive outside: a signed distance function. The folds are confined to where it is negative, the double contour is drawn where it equals two small negative values, and the lateral (Sylvian) fissure is carved in as a thin groove.

The cerebellum, a closed spline in proportion to the cerebrum and tucked under the occipital lobe, is filled with the phase plane of the FitzHugh–Nagumo model, the classic reduced two-variable model of a spiking neuron, due to Richard FitzHugh (1961) [4] and Jin-ichi Nagumo and colleagues (1962) [5]:

Here plays the role of the membrane potential and of a slow recovery variable. With , , and , the phase plane shows a stable limit cycle (in bold) and streamlines of the vector field: starting points on a jittered grid, each traced a fixed length forwards and backwards along the direction of the flow.

The brainstem is an integral sign, : a Catmull–Rom spline [3] drawn as a bundle of 21 parallel fibres, slightly thicker where the pons would be. It sits just in front of the cerebellum and curls back where the medulla meets the spinal cord; towards the top it passes under the temporal lobe and fades out, as the real brainstem disappears beneath the cerebrum.

The site is set in IBM Plex: IBM Plex Sans for titles and headings and IBM Plex Mono for text. Plex was designed by Mike Abbink at IBM with the type foundry Bold Monday, and is released under the SIL Open Font License. The equations are typeset by XeLaTeX in IBM Plex Mono Italic, with the symbols Plex lacks taken from Fira Math by Xiangdong Zeng, released under the SIL Open Font License.

The colours come from Nord, a palette by Sven Greb (Arctic Ice Studio), released under the MIT License.

The site is built with Jekyll and hosted on GitHub Pages; its source is public. The logo is generated by Python with NumPy, Matplotlib and contourpy. The website and the logo were designed and coded in conversation with Claude, an AI model made by Anthropic.

1. J. Swift and P. C. Hohenberg, “Hydrodynamic fluctuations at the convective instability”, Physical Review A 15, 319–328 (1977). doi:10.1103/PhysRevA.15.319
2. S. Pajevic and C. Pierpaoli, “Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain”, Magnetic Resonance in Medicine 42, 526–540 (1999). doi:10.1002/(SICI)1522-2594(199909)42:3<526::AID-MRM15>3.0.CO;2-J
3. E. Catmull and R. Rom, “A class of local interpolating splines”, in R. E. Barnhill and R. F. Riesenfeld (eds), Computer Aided Geometric Design, Academic Press, 317–326 (1974). doi:10.1016/B978-0-12-079050-0.50020-5
4. R. FitzHugh, “Impulses and physiological states in theoretical models of nerve membrane”, Biophysical Journal 1, 445–466 (1961). doi:10.1016/S0006-3495(61)86902-6
5. J. Nagumo, S. Arimoto and S. Yoshizawa, “An active pulse transmission line simulating nerve axon”, Proceedings of the IRE 50, 2061–2070 (1962). doi:10.1109/JRPROC.1962.288235