Reproduction

Reproduction
By an idea of Piet Ruhe

Hi Mira,
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.

Mira Solution

Mira ?!?
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!
Noooooooo!!!!!!!!

Sexehex Reproduction

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?)

6.th Generation

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The day after

We could represent the fractal with the true Sexehex:

True Sexehex Fractal

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:

Albert Einstein said

The idea of Piet Ruhe is not trivial.

First: He saw the full-hexagonal form of the SexeHexeS that so much people didn't see (and nor did the author!).

Second: The drawings are enchanting.

Third: The grid is a Fractal Grid!!!

The Hexagonal Fractal Grid

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.

Half Hexagon Sexehex Form

Last but not least: it's correct that a sexed form reproduces.

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Two days after
The Fractominoes

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.

The Sexominoes become Fractominoes

Below there is the second bi-bi-sex Sexomino:

The 2.nd Sexomino

Many Order(n^2) PolyOminoes could generate a fractal, but none does it more simply than the Sexehex "FMFMFM". (I think!)

16-ominoes become Fractominoes

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Three days after
The Fractalcubes

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.

A SexCube

But if you use it to make a reproduction of itself, you obtain this construction:

The SexCube germinates

Let me try with a 3x3x3 SexCube:

The 3x3x3 SexCube germinates

Each generation could fill the space.

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A curiosity:

In 2D A don't enter in B

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.

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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:

3 hexagon tile