It's definitely not as good as @joecooldoo's, but I tried!
I actually kind of like that!
that looks really cool too
might be even better!
What I like about it is that it captures the spirit of the variable-width swoosh at the top! But, as I said about @joecooldoo's version, it would benefit from using the actual Candara font for the blue part rather than drawing your own letters.
I've converted the ~1000x600px logo from LaTeX sources help\manual-LaTeX\common\logo.png
with https://www.pngtosvg.com/
But, although that's svg format, it still really has a bitmap inside, so it doesn't have the scalability of a born-vector version.
It looks a bit like spray paint over a stencil or something like that.
No, the body of the SVG contains only path elements, not bitmap
<svg id="svg" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="400" height="219.71356360572872" viewBox="0, 0, 400,219.71356360572872"><g id="svgg"><path id="path0" d="M163.195 0.261 C 159.574 0.367,156.557 0.539,156.492 0.644 C 156.427 0.749,155.063 0.906,153.462 0.995 C 151.860 1.083,150.549 1.242,150.549 1.347 C 150.549 1.452,149.907 1.538,149.121 1.538 C 148.335 1.538,147.692
To check this I removed "path0" element and altered path1.fill="#ff0000" . Result
Huh, okay, although all those numbers come from pixels. Does it scale well?
Another sense in which it retains its bitmap origins is that the file is huge, like the bitmap files, and unlike the much, much smaller files the children are making. 
The lines of the bitmap source are interpolated by a polygon with hundreds of points.
Lines can be smoothed by a better tool.