
I have a copy of The Magic Machine on my shelf which I (unintentionally) stole from my university library at the end of my senior year. His work was pretty influential on me, inspiring me to keep exploring programming at a time when my day to day work in the subject was often painfully boring.
https://www.springer.com/gp/book/9781461283492
https://www.springer.com/gp/book/9783540158516
Two other books that I think are good (but which are for general audiences) are AK Dewdney's Magic Machine which has a chapter about L Systems: https://www.amazon.com/Magic-Machine-Handbook-Computer-Sorce...
And Computers, Pattern, Chaos, and Beauty by Clifford Pickover: https://www.amazon.com/Computers-Pattern-Beauty-Clifford-Pic...
2a) build up a portfolio of programming stuff to show you can program
2b) that portfolio should also demonstrate polite professional communication skills. People discriminate against age (both too young and too old). They shouldn't, but this portfolio might help.
3) Get hold of any of these books, and implement the examples in a modern language.
Computers, Pattern, Chaos, and Beauty by Clifford Pickover (anything in this would be a good ShowHN, especially if you put it on a website with interactive sliders) (it's available as a download somewhere)
Any of the A K Dewdney books eg The Armchair Universe or The Magic Machine.
The fractals need only a few lines of code, with a bit of extra boiler plate. Tweaking the formula can give dramatically different results. You get to use a variety of programming concepts in a short program.
Relevant books are
Dynamical Systems and Fractals (Karl-Heinz Becker, Michael Dörfler) (This book has extensive Pascal code) http://www.amazon.co.uk/Dynamical-Systems-Fractals-Computer-...
http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511663031
Fractals - Images of Chaos (Hans Lauwerier) (This book has an appendix of BASIC code) http://www.amazon.co.uk/Fractals-Images-Chaos-Penguin-Scienc...
Sadly neither book is suitable for general 11 year olds, but a modern version certainly could be.
And A.K. Dewdney obviously has a bunch of books which could be used to inspire young programmers. The Armchair Universe, or The Magic Machine and similar launched many programmers, with "Core War", "Wator", "Bugs", etc
I seem to remember doing a very blocky Mandelbrot set on a 286. Good times!