Shrubs and flowers grow and flourish at different rates and it's this property that is taken advantage of in the idea named Einstein's Raised Beds.

The idea is simple: to plant a range of flowers that display some well known mathematical equations that take the form of strong graphic numeral and
letter shapes.

During the yearly season's cycle, the solution to the equations gradually emerges as brightly coloured late season flowers and leaves.

using genes to do logic: Gene Logichttps://science.sci...ontent/340/6132/599 We realized permanent amplifying AND, NAND, OR, XOR, NOR, and XNOR gates actuated across common control signal ranges and sequential logic supporting autonomous cell-cell communication of DNA encoding distinct logic-gate states. The single-layer digital logic architecture developed here enables engineering of amplifying logic gates to control transcription rates within and across diverse organisms. [beanangel, Apr 29 2021]

I really like this - it's practical, wouldn't be that hard to
implement, and has a pleasing surprise factor. Thinking
about it, I realised that I keep posting 'hidden message'
ideas (see links) which probably explains why I like it.

If you were a disgruntled gardener, it would be
pretty easy to plant seeds spelling out offensive insults to
your employer and then resign, knowing that the insults
would appear some months later.

I was hoping that the planting would demonstrate the equations more viscerally, for example by growing at certian rates so the ratios between adjecant plants would be... um...

That's a beautiful thing, but I was thinking more about proving
Goldberg's Conjecture. As an unsolved problem, your proof may
ultimately fit in a very small allotment - but getting to that
point might cover a lot ground.

(edit to add - I do see it already has some consideration <link>)

If your garden was nearly infinitely big, it should be possible to turn
the planting in a garden into a Turing machine. Then you could use
your garden to compute any computable problem, which would be
cool

What about getting plants to actually solve equations? As a
slow computer, but one that doesn't require working with
silicon at nano-scales. The interface may be a little
complicated to figure out.

Yeah, I was rather hoping that this would make more use of
the plants' internal mathematics: things like the fibonacci
sequence appearing in successive rings of petals, and plant
growth rates being a function of ... other things, and
bindweeds describing spirals, and trees representing tree
structures. That sort of thing.

//Yeah, I was rather hoping....// Just write it up
and post it now that you see the light. I wanted to
create something that could actually be
constructed and realised, albeit with a lot of
careful planning and effort. I'm sure, just like the
monkeys with their Shakespeare generating
typewriters, that given enough plants,
configurations and time, Fermat's last theorem
would magically be solved in a greenhouse. Magic
solves all problems.

Or external mechanics. Say a 50km square 'Game of Life' but in flowers. The computation would be visible yielding a summer snapshot in flowers of how far the computation is going. When you end up with a 50km sized '42' visible from space, its ready.

Slime moulds have been proven to have a superior
problem solving ability within a system. (Look up
slime mould learning the most efficient way to
navigate the Tokyo underground - (link) I'm sure
someone
could construct a slime mould computer.