By an idea of Piet Ruhe
Do you remember that night? It was the 28 Mar 2000. You was testing your solver with the SexeHexeS and I said you: try to solve the triangle, but left out the "MFMFMF".
Do you remember? You sent me the solution after 1/2 hour. It was midnight.
A great solution! Your solver is really powerful.
Are you listening to me?
Mira, where have you put that piece?
The "MFMFMF". Mira! Mira! Mira!
Don't joke. That piece is trisexed. It reproduce, worse than an Italian!
Tell me you haven't forgot it in the culture broth!
It does a generation every second. Its surface is multiplied by 4 every generation. Its original surface of 1 cm2 becomes 1 Km2 in 16.61 seconds. In 31.07 seconds it covers the entire Earth!
We are f... (how do you say in English?)
The day after
We could represent the fractal with the true Sexehex:
I preferred to draw it with its full-hexagonal form because it seemed me simpler, linear and elegant.
For this simplicity, a famous Mathematician said me:
"Your hexagonal fractal must be old (it's generated by such a simple rule)"
A famous Phisicist said the same thing:
The idea of Piet Ruhe is not trivial.
Notice below the hexagonal form of the SexeHexeS. They seem to the PolyHes of Andrew Clarke, but they are an other thing. They have a 'baricenter' on a triangular grid, as the 3 colors painting proves.
Two days after
The ideas also reproduce.
Nothing is so concrete as the thought. [Democrito]
If 2+2=4, a Sexomino must to germinate. I think there are 3 SexeHexeS and 2 Sexominoes that could germinate. Notice that they aren't 'Reptiles', because they don't reproduce the exact form, but the male/female concept.
Below there is the second bi-bi-sex Sexomino:
Many Order(n^2) PolyOminoes could generate a fractal, but none does it more simply than the Sexehex "FMFMFM". (I think!)
Three days after
If 2x2x2=8, a SexCube must to germinate. Below there is an octacube that you could see as sexcube 2x2x2. Normally it could fill the space.
But if you use it to make a reproduction of itself, you obtain this construction:
Let me try with a 3x3x3 SexCube:
Each generation could fill the space.
In a 2 dimensions world, A don't enter in B. To insert A in B, you need the 3.rd dimension . It's the same thing for the FractalSexCube. If you want to insert a FractalSexCube in an other, you need the 4.th dimension, for example a space-time jump. If you don't have a space-time jump then you could try with a hammer.
_________________August 15th, 2000
2D simplest possible fractal
The sexehexes fractal has a simpler version, inspired from an Italian floor that I have seen the last holiday:
If you represent the three hexagons with the baricenters, probably you get simplest possible 2D fractal:
First edition: 23 June 2000
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