Desmos Animation 101: Part 2

Suzanne von Oy shared a graph titled The Tree of All Seasons awhile back as one of her #graphjam submissions. It's mesmerizing at the very least, and left quite a few of us wishing for a Desmos art course so Suzanne can teach us her magic.

I look forward to this course, but as I dove into the graph, I found myself quickly overwhelmed. So many variables and functions. I wasn't sure where to start with understanding the various parts. This left me wondering what the different parts are of the Desmos art course that will allow me to build this (and any) awesome graph.

So where would the course start? There are quite a few things going on just with the flowers in The Tree of All Seasons graph.

1. The flowers are all different sizes. Suzanne uses exactly one image to render all of the flowers, so I'm curious as to how she made them all different sizes.
2. The flowers start growing at different times. They start falling at different times. They start shrinking at different times. I imagine these are all related somehow.
3. Once the flowers shrink down to size zero, they stay at that size throughout the animation.

In my first post, I looked at the way in which we can control the size of the flowers using a function. In this post, I want to look at the way in which we can control the timing for which the flowers bloom and shrink.

I stared at this line of Suzanne's graph for a really long time.

After breaking it down and figuring out that the first expression (in parenthesis) assigns each flower its length and width depending on its y-value, I looked at the second expression and thought about what it does:

If I graph this I see the following:

This graph assigns a "size" to the flowers depending on time. It essentially says the flowers will grow from size 0 to full size (or size 1) in a certain amount of time. Then the flowers will stay full sized for a different amount of time, after which they will shrink down to size 0 and stay that size throughout the animation. Super useful!

Question: What are other uses of this function that people might explore before working on the The Tree of All Seasons problem?

Note: I am interested in exploring what a Desmos art/animation course would look like for personal reasons, but also I am interested in exploring what it would look like because I'd love to see a course like this offered at the high school or college level as a math elective.