Math & Science ⇒ Help: Creating Pascal-esque triangle (different structure and numbers) with TikZ for academic paper

[spe420]

I am new to using TikZ, but have been using LaTeX via LyX for several years now. While I am not the most adept user, I am somewhat confident in my understanding of how the program works, albeit unfamiliar with all of its features. I understand this is a fairly high level task to try to implement, but I have very concerted reasons why this is my immediate aim.

I do not think the details of my project are entirely relevant or necessary to explain, however, I will say this:
–I am writing an academic paper that I hope to be able to submit to arxiv.org in the area of Number Theory;
–I have the vast majority of the paper written, with the exception of this particular diagram and an addendum to the end;
–I have recently purchased the LaTeX Cookbook, as well as LaTeX Graphics with TikZ, and have numerous other resources;
–I am willing to take the time necessary to under to learn the concepts, but have only limited coding experience (and via GUI in, LabVIEW).
Any assistance would be greatly appreciated.

The basic problems I need help with are:
1) some practical advice about most sensible workflow (I have read about so-called ERTs, and using text editors, etc. to insert "child documents" in LyX, exporting from CAS programs (I have installed Maxima, but yet to really learn how the program works);
2) how to make customizations to the generation of Pascal's Triangle-like structures (I have watched this tutorial:
https://www.youtube.com/watch?v=V1XBdHdofuw) such that, for example, I can stipulate the diagonal "column" containing the terms which would otherwise be the binomial coefficients k=0 (the left-most infinite series of ones), as being numbers generated according to a particular formula of my choosing, each successive diagonal row extending from the terms in the right-sided row of the triangle (i.e. the infinite series from n=1, k=1 down and to the left, and so on), being self-similar in their ratio to those terms contained in the first, with each term in the right-sided row (i.e. from n=0, k=0 down diagonally to the right) being the powers of any given input x, such that x^0=(n=0, k=0), *EDIT* x^1=(n=1, k=1), x^2=(n=2, k=2), etc. *EDIT*. I hope I have explained this adequately.

I understand this may be a very difficult problem... I have already begun, with some chagrin, to appreciate how difficult it is going to be to use this as a pretext for learning TikZ, and more of the fundamentals of LaTeX, but it is, I think, the only way to finish my paper as I have envisioned it. Any help that would be so graciously offered would be invaluable.

[Stefan Kottwitz]

Hi,

welcome to the forum!

I'm glad you got these books. I wrote them, and I'm happy when I hear that people read the books. I hope you liked them! Would you please be so kind to post a review for each on Amazon? (even if you got them in another bookstore). Reviews help me find readers and convince my publisher to allow me to produce another, extended edition. I want to create an extended edition of the TikZ book, so reviews would be greatly appreciated. For now, I made a Japanese translation (see TikZ.jp) and I'm working on a Japanese translation of the LaTeX Cookbook.

Regarding the workflow, I think that when you get more experience with LaTeX, you may switch from LyX to a LaTeX editor, such as TeXstudio or TeXworks. With a good template, you may not need LyX anymore. Compiling is fast nowadays, allowing you to track progress in a LaTeX editor that displays Code and PDF side by side. When I create TikZ pictures, I often compile them every few seconds to see the changes as I adjust. But LyX is good with ERT for now, of course.

I saw the Pascal triangle video. It's a short piece of not much explained code, but basically it is

• a \foreach loop for the rows
• a \foreach loop for the columns
• a calculation for the coordinates of the nodes from row n and column k
• a pgfmath calculation for the value in the node text

You can make it similar. If you like, share your code here and I can help improve it.

As your focus is on the paper as a result, and not on a TikZ code, you could also simply use tabular or array and put the calculated values in, using Excel for example. Ultimately, it's the PDF that's important, not the smart code, especially if there's a time pressure.

Stefan