Peaucellier's linkage

This is an interactive CDF of the Peaucellier's linkage. A better illustration is on the Wolfram Demonstration project by Izidor Hafner.

I explore this linkage in Walking in a straight line.

How do you see the world

Someone introduced me to the joy of the xkcd site. I found this strip particularly entertaining. This prompted this post.

You can click on the map and you will be taken to the wikipedia entry about the projection (if there is one) or to a page that allows you to search. The Eckert projections do not have entries but really it is the fault of my code.

Newton's method: basins of attraction colored by root

In this post, I have modified the previous code to color points in the basins by the root they converge to and diverging points differently. The contrast (and consequent clarity) varies by color scheme.

Newton method: basins of attraction

This post is inspired by Invitation to Mathematics. The graphic is a ListDensityPlot of the number of iterations of Newton's method to find root till convergence (using length of the list from FixedPointList function) for points in the complex plane (the unit square). The polynomial is a cubic with roots zero, 1 and the parameter point. The roots are seen as the left and right lower corners and the point in the Slider2D. Gradient color schemes are used to represent the convergence. The basins of attraction are,therefore, illustrated as well as the set of points whose orbit diverges. In future posts, I aim to color the basins for the particular root.

Morse code