Dynamic Visualizations

The site now has the capability to include p5.js sketches into blog posts. The framework enables math+art to provide visualizations of mathematical concepts in fun ways. For example, let's take a look at a simple example of sinusoidal motion.

This square's position oscillates via a sinusoidal function of time. Given the height $h$ of its container, the square's $x$ position behaves as

p5.js provides a nice interface to bring this equation to life. Similarly, we can visualize circular motion — and while we're at it, let's reduce the velocity too.

That one's coordinate positions are

Finally, we can combine the two motions, i.e., $x(t) = x_s(t) + x_c(t)$ and $y(t) = y_c(t)$.

While these examples just scratch the surface of what's possible with p5.js sketches, I look forward to including more advanced and interesting visualizations in future posts.