Backstory please.
We then went wild buying shirts for the family, a sticker (stuck currently on the water filter in the living room), a mug which was supposed to be mine but which my son guards as a precious possession, and a giant wall tapestry to hang in my son's room. I actually wasn't sure all of those were going to come out, but even on the sticker, you can make out the individual cells in the more complex designs. Anyway - we enjoy these things on a daily basis.
We're kinda a bunch of math geeks. My husband and I both have masters degrees in the field, and our son, I guess, is a demonstration of what you can accomplish with selective breeding. ;) We have a lot of mathematical curiosities around the house, most of them homemade - penrose and hat tile fridge magnets, klein bottles, constant width solids, representations of projective tuning space. You know, the usual.
Other enthusiasts in the (very niche) space enjoy seeing the graphic. Since the time of creation, math has advanced, with these no longer being the smallest or best examples of some of these loops. This is exciting for all of us - the advance of mathematics is usually not this accessible. :)
This kid's scratch page is wild - https://scratch.mit.edu/users/noonagon/
One of my favorite joint projects with him was a python implementation of Game of Life in which individual cells have velocities, and will crash into and react to each other. He just came up to me yesterday proposing a refinement to the physics. I oughta put that one up on Github. Good times. :)
Kids.
Because this is amazing
We just hope they choose to use their powers for good.
I can also recommend Snap Circuits for Christmas. :)
And you get to build lots of cool circuits. Designing your own isn't hard, you can get really far with just op-amps and resistor/capacitor circuits.
some of the resistors are potometers, of course. So you have some knobs to turn.
But it is usually bog-standard chips. op-amp, simple gates, 8-bit buffers.
My son (just turning 7) is smarter than I am; and possibly more as an artifact of being on the spectrum, is nearly bored after textual representations ( one tredecillion, ten tredecillion...), ~70 digits of pi, latin/greek alphabet, periodic table, planets/cosmos, and every other aspect of rote memorable/science/math things.
I'm not sure if he's bored now, or simply too busy with trying to learn to read, or burnt out, but I've tried to look for more collegiate material that may suit him, besides looking ahead 4-5 school years, and come up rather short. Some private tutoring material has seemed most helpful, but so far, YouTube has the best material, but obviously that has its own issues.
Besides more moderated Youtube/Kids, i fear im missing something obvious
What we did in past years was, largely, giving him unfettered access to math and math-related channels on youtube. Vi Hart, Numberphile, 3blue1brown, stuff like that. When he showed interest in something specific, we'd get him appropriate materials. Since his elementary school was a public montessori school, his teachers encouraged us to send him with appropriate math workbooks for his capability level.
"What if there is no Internet?" No computer? Etc...
Papa (grandfather now, raising my granddaughter because... not important, lol) tends to impress the young ones with what can be done with what is in one's head.
I am hopeful. But maybe also naive.
The other idea I like to link to these skills is "thought is action" type mastery. And, just to be clear, that is a state of clarity coupled with having grokked[0] something valuable.
Having realized that state many times in my past makes it easier today. I can go there and perform, doing or dealing with whatever it is efficiently and effectively.
It also can mean agency where ones peers may well lack it.
[0] - ...having achieved a state of understanding so complete it is a part of us, who we are, automatic, almost instinct.
Fascinating few years, a whole generation of designs rendered unusable - complete designs trying to be reworked for the chips they could get a hold of.
Of course then they promptly went and discovered spectre tiles.
I have since fixed my 3d printer. And it occurs to me that that does open up a rather obvious option for a Christmas present.
There's this to help create non-overlapping tilings, but understanding it is completely beyond me (or the amount of time I have to invest, I tell myself...)
https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperi...
This module, for example https://www.nonlinearcircuits.com/modules/p/cellular-automat... uses networks of XOR gates to create "is a 16 cell gate and pattern generator using cellular automata rules 90 & 150".
Blinky lights in a grid that steps with those rules and can steer other modules.
I love mine.
The designer has many other wild designs based on chaotic dynamics and many other non-linear mathematical concepts. The name is kind of a giveaway.