This page is just for fun. These are a few pieces of generative art made in Python: strange attractors, chaos-game fractals, and a rendering of stream density across the United States. Click an image to view the full-resolution version.Strange attractors, Sierpinski triangles, and stream density, all rendered in Python with matplotlib.**A few notes on the pieces:** - **The Lorenz attractor** is the classic "butterfly" produced by the Lorenz system of three ordinary differential equations, a simplified model of atmospheric convection. The system is famously sensitive to initial conditions, so many trajectories started at slightly different points are traced through phase space and layered on top of one another. - **The Clifford attractor** is generated by repeatedly applying the transformations $x_{n+1} = \sin(a y_n) + c \cos(a x_n)$ and $y_{n+1} = \sin(b x_n) + d \cos(b y_n)$ and plotting the resulting points. - **Stream density** visualizes the density of stream reaches across the continental United States as a surface, viewed from above and from an angle. - **The Sierpinski triangles** are produced with the "chaos game": repeatedly jumping halfway toward a randomly chosen vertex of a triangle. The final piece connects each sampled point to its nearest neighbors.
