Bill Shillito

Using heuristics for the optimal solution to the game of Snake Using a combination of A* and a heuristic function to produce the optimal solution for solving the classic game of snake.

I mean actually yeah I think so! XD

hogg.io/projects/snake

I hadn’t even thought of Snake!

Anyone have ideas for games (especially combinatorial ones) that inherently involve taxicab geometry? Not just games that happen to take place on a square lattice but where taxicab distance is actually an important part of playing the game?

The math educator to Balatro addict pipeline is real

Oh yeah we do need to talk about that again!

Who’s going to be at #MAAthfest next week? Let’s meet up!

Oh this looks AMAZING. 🤩 Anything is better than the smoke, mirrors, and duct tape that is TikZ.

I'm putting "rigor" in scare quotes.

My dissertation is officially uploaded, so I finally feel like I can say I have my PhD! 🥳

scholarworks.gsu.edu/entities/pub...

It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!

A picture of Le Poisson Steve (an orange fish with arms and legs). Above his head is the probability mass function for the Poisson distribution: P(X = k) = λ^k e^-λ / k!.

Le Poisson Steve

Alternatively, *start* with Taylor series and their uses (new integrals unlocked!), and fill in convergence tests afterward when something goes wrong with one of them and we need to know why. 🙃

A infinite stack of bLue and Red chips. Each bLue chip is labeled with an L, and each Red chip is labeled with an R. The stack from bottom to top is labeled LLLLRRRRLRRR... . Below it, the value of π is given as follows: π = { 0, 1, 2, 3, 3 1/8, 3 9/64, ... | ... , 3 5/32, 3 3/16, 3 1/4, 3 1/2, 4 } BRIEF GAME EXPLANATION: Stacks is a simplified version of Hackenbush. The original concept comes from Carl Lee at University of Kentucky, who calls it "Checker Stacks." The game starts with some number of stacks of bLue and Red chips on the table. On your turn, you can pick any chip of your color and remove it from the board, along with any chips of either color on top of it. If your opponent can't move, you win. The notation G = { L | R } specifies a game value in terms of the sets L and R of possible values when bLue and Red respectively make a move. If G is a number, then the value of the game will be strictly between the elements of L and R, and hence the sequences listed converge to π from above and below.

Happy #PiDay! To celebrate, here's my favorite representation of π: as a position in the combinatorial game of Stacks.

Infinity is still my favorite number. 🙂

That’s why I teach limits at the end of Calculus I instead of the beginning! 🙂

A toroidal hush puppy. It looks like an onion ring, but it was, in fact, a hush puppy.

Something seems off about the Euler characteristic of this hush puppy.

YouTube video by Owen Maitzen HACKENBUSH: a window to a new world of math

Combinatorial Game Theory!

This video is the essential introduction to the subject. Probably one of the most beautifully produced math videos I’ve ever seen. It’s what cemented my interest and sent me down the most fun mathematical rabbit hole I’ve ever found!

youtu.be/ZYj4NkeGPdM?...

A computation showing that if G = {*, ↑|↓*, 0}, then G + G = *, so G is usually called “semi-star”. The computation involves looking at all moves from G + G and showing that they’re “reversible”, that is, any move by a player has a response that puts their opponent in at least as good a position. In this case, a move to * can always be reversed to 0. In the process, we get a picture of G’s confusion interval: G is confused with 0 and ↑, but also confused with * and ↓*. This lets us picture where G lives on the “number line” (using scare quotes because none of the games on the board are numbers in the game theoretic sense except for 0).

Apparently this is now what I do for fun when I need a break from work. 😂

I'm not following...

If I ever ask students to sum an infinite series by asking “what the sigma” I ask that you please slap me

using the Vine boom to emphasize points in a lecture

Happy (20 + 25)² :D

Left: Garlic deviled eggs (toum [Lebanese garlic sauce], mayo, dijon, green onion, topped with chives and cayenne) Right: Ramen deviled eggs (miso, mayo, honey, topped with furikake, and the whites have been marinated like onsen eggs)

This year's deviled eggs for #NewYearsEve!

Left: Garlic deviled eggs (using toum!)
Right: Ramen deviled eggs (made like onsen eggs but hard boiled)

It helps to know I’m not the only one having to do this.

NAILED IT

A formula sheet for abstract algebra next to a breakfast sandwich and coffee.

About to take my final for Abstract Algebra (group and field theory).

If this goes well it will be the *last* final I ever have to take.

LET’S GO! 😎

Welp I know what I’m adding to my portfolio assignment next semester.

For great justice.

Figure 19: The thermograph of "oof". A horizontal line is marked with 0 in the middle, "on" to the left, and "off" to the right. A second line diagonal crosses 0 and continues upward and to the right. The region under the diagonal line and above the horizontal line is shaded, with {0 | off}, the canonical form of "oof", written in that region.

Presented without comment: The Thermograph of "oof".

Optimist: The cup is half full.

Pessimist: The cup is half empty.

Combinatorial game theorist: The cup is a win for Left, because she can take it to the zero cup. If Right moves, he will take it to the one cup.

A poke bowl made with romaine lettuce, brown rice, and topped with salmon "noodles." Arranged around the edges clockwise from the top are seaweed salad banchan, spicy squid banchan, hard-boiled egg slices, grape tomatoes, green onion, spicy octopus banchan, mashed avocado, and red onion. The top is drizzled with sriracha mayo and gochujang and sprinkled with furikake. To the left is a pair of disposable chopsticks propped up on a holder made from their wrapper, and on the right is a glass of mixed berry juice with ice.

Here's an entry for #GoodLunch!

wild how the english alphabet ends with xyzw