![]() ![]() Plotted something interesting that's not on the demo? Used my code in your own project? I'd love to see it! Intuitively, think of z n as r ne i n phi.Ĭontourer provides an easy way (well, provided you know GLSL) to plot any of these, and more! It shows how the plot of z n changes as n increases from 1 to 4. For Complex Exponentiation, the plot is in polar coordinates rather than Cartesian coordinates to make the effect clearer.Once again, read Visual Complex Analysis by Tristan Needham to learn more. This illustrates the conformal (angle-preserving) geometry of holomorphic (complex-differentiable) functions. Observe that, for all complex function demos other than Complex Exponentiation, the mesh lines form square-like cells.Complex functions transform a point on the complex plane (a complex number) to another point on the complex plane.Using simplex noise (PDF) (a better version of Perlin noise) to warp terrain is described in this GPUGems article (under Sampling Tips, section 1.3.3).Procedural terrain generation may assign a small 2D deformation to each point in 2D space for more interesting terrain.Galaxy Warp is inspired by the old theory of differential rotation in galaxies, which is not how galaxy arms are formed.2D classical physics maps the initial position of a particle in 2D space to its final position in said space.This is inspired by colah's post on neural networks and manifolds.Neural networks with 2 input neurons and 2 output neurons map 2 real numbers to 2 real numbers.Read Visual Complex Analysis by Tristan Needham to learn more. This is made possible by the equivalence between the multipole expansion and the Laurent series.The demo shows electric field lines in blue and equipotential lines in red.( Dipole Formation, Attraction to Repulsion) 2D electric fields assign a 2D field vector to every point in 2D space.In Mercator (the most popular world map projection) to Mollweide (an equal-area projection), we see graphically how land area is distorted on world maps.Map projections transform lat-long coordinates to a point in 2D space.Lorentz Boost shows, according to special relativity, the spacetime warp an observer experiences when his velocity changes.This is how graphics programming works.2x2 matrices transform 2D vectors to 2D vectors.What are 2-input, 2-output functions, you ask? Here are some examples: Contour graphing is an excellent way to visualise 2-input, 2-output functions. ![]()
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