These are all screenshots of my Excel spreadsheet! You can download the spreadsheet from my blog.

New blog post! I used ChatGPT to help me create a Mandelbrot set in Excel! Here are the 30x30, 60x60, and 250x250 versions. I'm also including a few zoomed-in views. divisbyzero.com/2024/11/13/m…

Some different bases for numbers and who used them. Base 10: Egyptians Base 60: Babylonians Base 20: Mayans Base 2: Computers Base 16: Computers Base 26: Microsoft Excel

Here's a fun little "magic trick." Can you figure out how it works? Hint: even and odd numbers. I was thinking you could roll a die to determine how much to count each time. (I saw the trick was credited to Martin Gardner—true? Source?) youtube.com/watch?v=DaWcL3oO…

typed in my request and pasted a screenshot of the equation from the article. Within five minutes, it was plotted! I then took a true cardioid, scaled and translated it so it was atop the other heart-shaped curve. As you can see, they are nearly indistinguishable! 4/4

smaller heart-shape is the image of the unit circle under a messy complex map (see below). ams.org/journals/proc/1995-1… I wanted to see it with my own eyes, but I didn't want to have to figure out how to graph this beast. So, I asked ChatGPT for the code to graph it in Sage. I 3/4

Here's another neat generative AI example. It is well known, and not hard to show, that the main component of the Mandelbrot set is a cardioid. Looking around the Mandelbrot set, you'll see other cardioid-looking shapes. On the right, you can see the largest one. People who 1/4

Here are my attempt to get Dall-E to make a "Mandelbrot[wurst]" or "[Mandel]bratwurst."

I decided to make a little video using @geogebra illustrating the relative sizes of the planets, the orbits of the planets, and an assortment of stars (including WOH G64, the largest star of known radius—1540 times the radius of our sun!).

I updated my arXiv article "How much string to string a cardioid?" (again) arxiv.org/abs/2311.15101. It now has a new result. For a "nice" number (like a prime number) of points n in a circle of radius r (and any multiplicative factor a), the amount of string required is