Iterated Weighted Arithmetic Means

Posted on January 19, 2023January 19, 2023 by Sam

This isn't a novel idea, but I was looking for an iterative method for easing between two values. In this post, I describe and analyze the method of iterating a weighted arithmetic mean. I'm going to examine the effect of changing the weight factor and the rate at which the limiting value is approached as iterations increase. The end goal of this is to provide an alternative easing method to the standard parametric methods that use easing functions such as smoothstep or logistics. This allows t...

Collection of Desmos Graphs – Part 4

Posted on December 31, 2022December 31, 2022 by Sam

In a Desmos Global Math Art Contest-induced fit of madness, I almost forgot to do the annual Desmos graph showcase. But it's not 2023 yet (hours away!) so nobody can say I didn't do it. From harmonographs and obscure coordinate projections to artistic animations, this has probably been my most active year with Desmos, which is really saying something, since it has been my primary hobby for quite some time now. As such, attempting to comb through and select only a few graphs that represent the y...

Computational Geometry and Topographical Maps

Posted on August 11, 2022August 13, 2022 by Sam

Everyone has seen a topographical map at some point during their life. In addition to the information that regular maps have, topographical maps typically show land features and elevation. How are these maps generated? Given that it's not possible to sample the elevation at every single point in the area of interest, we must use some sort of interpolation. To tackle this mathematically, we should make a few simplifications. As you might agree, the Earth is round. However, if we consider the ...

Collection of Desmos Graphs – Part 2

Posted on December 30, 2020January 2, 2021 by Sam

Just like last time, I'm going to share a few of my favorite recent graphs on Desmos. This is probably going to become a yearly thing - despite that the previous part was my first post ever, it remains the most popular. That's probably due to the fact that r/visualizedmath on Reddit won't let me post anymore to share my work. Anyway, on with the graphs... November 2019 MCC Puzzler Try it yourself: https://www.desmos.com/calculator/qsy5qk4sjv Last year, I took a couple math classes...