Physica D: Nonlinear Phenomena - Analog computation with dynamical systems. 23 Mathematical Challenges. Professional/usenixsec2012-rubberhose.pdf.
El Patrón de los Números Primos: Prime Number Patterns. By Jason Davies. For each natural number n, we draw a periodic curve starting from the origin, intersecting the x-axis at n and its multiples. The prime numbers are those that have been intersected by only two curves: the prime number itself and one. Below the currently highlighted number, we also show its sum of divisors σ(n), and its aliquot sum s(n) = σ(n) - n, which indicate whether the number is prime, deficient, perfect or abundant. Based on Sobre el patrón de los números primos by Omar E. Pol. Smooth Voxel Terrain (Part 2) « 0 FPS.
Last time we formulated the problem of isosurface extraction and discussed some general approaches at a high level. Today, we’re going to get very specific and look at meshing in particular. For the sake of concreteness, let us suppose that we have approximated our potential field by sampling it onto a cubical grid at some fixed resolution. To get intermediate values, we’ll just interpolate between grid points using the standard trilinear interpolation. This is like a generalization of Minecraft-style voxel surfaces. Our goal in this article is to figure out how to extract a mesh of the implicit surface (or zero-crossings of ). Marching Cubes By far the most famous method for extracting isosurfaces is the marching cubes algorithm.
Much of the popularity of marching cubes today is due in no small part to a famous article written by Paul Bourke. Paul Bourke’s exposition is really good. This last point needs some explaining, Conceptually, marching cubes is rather simple. Marching Tetrahedra T. Algernon's Law. Loopholes Examples Pacemakers are an example of #3: evolution couldn’t afford to engineer more reliable hearts, in part for lack of electronic microchips and possibly because humans are already at the limits of the performance envelope.
Many traits related to nutrition fall into the category of #1. How about supplements? Most supplements are just tweaking biochemical processes, and don’t obviously fall under 1, 2, or 3; and the few which seem to enhance healthy humans are finicky creatures (see my introduction to Nootropics). Melatonin, for example, may seem particularly questionable as one’s body secretes considerable quantities in an intricate cycle (but see later). Flynn effect The Flynn effect is a possible counter-example: it operates broadly over many countries, improves average IQ by perhaps 10 or more points over the last century, presumably is environmental, and operates without any explicit expensive eugenics programs or anything like that.
Piracetam Isn’t this interesting? Melatonin. Www2.kenyon.edu/Depts/Math/Milnikel/boolos-godel.pdf.