Oh nice, I'll let you know!

I haven't, but good point. The code to count transitions between characters is very straightforward (well... I wrote mine without worrying about performance issues), and in principle could be packaged as a lightweight web app or even a JavaScript-powered static site and accept any text corpus uploaded or linked by the user.

Nah, I'm only just now getting a chance to edit my top-level comment. Thanks for throwing in your vote! I feel like I can reword the "interpretation" part better to avoid any possible misinterpretation.

It does if you include the placeholder "characters" for the start and end of each name! The most probable "name" A represents three tokens: [name start], A, [name end]. And if you generate many names using the transition matrix, you will indeed observe that the frequency of [name start] -> A and A -> [name end] matches the corresponding frequencies in the source data.

EDIT: on reflection, I agree with you. I should introduce the heatmap as a description of transition probabilities, but should avoid walking the reader through using the transition matrix to generate new "names." I should separate the topic of generating new names using the transition matrix under the (invalid) Markov assumption as a diversion. Thanks for pointing out the flaw in my explanation. I'll edit my top level comment when I have a chance!

The fact that names are not memoryless is exactly why treating them as such produces such entertaining results :)

Oh? What part? I specifically qualified my interpretation with "want to reflect typical between-letter patterns of US girl names."

That's the point of using this viz to generate new names: generating character strings with totally realistic letter-to-letter transition probabilities is not enough to yield plausible names, or names which already exist. The generated names are often bizarre or excessively long, yet their character transition probabilities exactly reflect that of the real names in the input dataset.

That 95 means that 95% of the time, a Q was followed by a U in a name.

Oh, absolutely: the fact that this Markov assumption yields nonsensical names shows that the sequence of letters in given names are not generated by a Markov process. (The next character depends very much on previous characters, not just the current one.)

But this visualization does accurately present the relative frequencies of character transitions in actual names. Using these frequencies to generate Markov chains of characters and calling the results names is a fun diversion whose results I found entertaining.

Yep. "A" is the most frequent letter at both the start and end of names in the dataset I used (girls born in 2021 in the USA).

Interpretation [EDITED]: Take all the names on U.S. Social Security card applications for girls born in 2021. Scan through the names one letter at a time, accounting for the start and end of each name. Count how many times each particular letter is followed by every other letter in the alphabet. Finally, convert your counts to probabilities (technically, percent chance = probability * 100%) to give the chance that any given letter in a name is followed by every other possible letter (or by the end of the name). This visualization summarizes the resulting transition matrix.

Background: The ongoing explosion of generative AI systems got me thinking about the statistical structure of words, and of given names in general. I started with the fairly basic idea of treating the sequence of characters in given names as a Markov process, i.e., the next state is chosen randomly according to transition probabilities that depend only on the current state, not prior states.

Code: https://github.com/pjleimbigler/baby-name-analysis

Data: https://www.ssa.gov/oact/babynames/limits.html

Generating new "names": The letters in given names are pretty clearly not generated by a Markov (memoryless) process. However, it's fun to assume the Markov property anyway and see what "names" fall out of the transition matrix.

To iterate through the transition matrix manually using this viz, follow these steps:

1. Start with the bottom row, (Name Start).
2. Each number in your current row is the percent chance (probability * 100%) of choosing your name's next letter as the letter corresponding to each column.
3. Randomly choose the next letter of your name, based on the percent chances in the current row.
4. The letter you just chose now becomes your "current letter." Look up its row.
5. Repeat Steps 2–4 until you land on the last column, (Name End), which signifies the end of your generated name.

This yields some hilarious yet often oddly plausible names, such as: Silian, Slya, Lialy, Maerollia, Chla, Zalah, Lay, Lonanaadievayle, Zoralepa, Peiemophaly, Dralesa, Wiada, Miea, Giaberosh, Bisodiaremanninenn, Seelanida, Einnn, Penasoetimala, Hepanelei, Mia, Mierolynakynisayloloneeloa, Sargandniamilida, Eldyanempe, Pinahanariloma, Alian, Melivevilllohayasisa, Olyna, Die, Mizaramiceatelyalla, Jon, Adelun, Cesklienzolena, Zolyryn, Ema, Leyla, Aclan, Bra, Maeylises, Bryn, Khiemi, Sly, Annnlis, Aisyasa, Xily, Kara, Handanaria, Manla, Pama, Heyanama, Eylisidr, Brah, Llee, Anelerynaevega, Ayatryalofa, Mediza, Caniesty, Oliceeelys, Sannllora, Dassole, Sonnasse, Mmatarieleteyneroselasylin.