Enzymind Labs

Absolute differences of progressive rule systems:

Progressive 1 |-| (Progressive 1)_rotate(pi)

Progressive 2 |-| (Progressive 2)_rotate(pi/2)

Progressive 2 |-| ( Progressive 3 |-| (Progressive 3) _rotate(pi/2) )

Progressive 3 |-| ( Progressive 3 )_mirror(x)

 

 

The following images are logical combinations of patterns generated by progressive 2x2 L-systems with constant rules. There are only three unique constant rule systems (labeled Progessive 1, 2 and 3 ), but many possible combinations when all mirrored and rotated images. Only a few logical operations and combinations are documented here.

The combinations shown are not necessarily unique -- there are other logical combinations that result in the same final image.

Single L-systems might describe these combinations, but if they exist I have not found them. Let me know if you have any ideas about this.

The algorithms are represented by a graphic which corresponds to this pseudocode:

{ start with a symbol
repeat for n_g generations:
{ replace each symbol with the corresponding symbol's rule }
perform rotations and/or mirroring
perform logical operations
}

Absolute differences of progressive rule systems

These systems are formed by subtracting the ordered symbols of two or more systems, elment-by-element.

Note that the absolute differences sign, |-|, indicates the absolute value of the differences of a pair of ordered symbols or an ordered symbol set, where the first rule is 0 (zero). So a - b = b - a, but a - ( b - c ) NOT= (a - b ) + c. I made-up this sign to try to be clear. I'm treating the symbols as members of a mathematical field, but I don't know the proper formalism.

P1-P1r180 , or Progressive 1 |-| (Progressive 1)_rotate(pi)

Absolute difference of Progressive 1 and Progressive 1 rotated by pi radians:

This is equivalent to:

( Progressive 3 |-| ( Progressive 3 )_rotate(pi/2) )_rotate(pi/2)

High resolution P1-P1r180 system image

P2-P2r90, or Progressive 2 |-| (Progressive 2)_rotate(pi/2)

Absolute difference of Progressive 2 and Progressive 2 rotated by pi/2 radians.

High resolution P2-P2r90 system image

Near both diagonals the pattern is similar to the Progressive 2 pattern, morphing to a different pattern at increasing distance from the diagonals.

P2_-P3-P3r90, or Progressive 2 |-| ( Progressive 3 |-| (Progressive 3)_rotate(pi/2) )

Absolute difference of Progressive 2 and the absolute difference of Progressive 3 and Progressive 3 rotated by pi2/ radians:

High resolution P2_-P3-P3r90 system image

This pattern has the character of Progressive 2 along the top-left to botton-right diagonal, and the character of Progressive 1 along the other diagonal.

P3-P3mx, or Progressive 3 |-| ( Progressive 3 )_mirror(x)

Absolute difference of Progressive 3 and Progressive 3 mirrored in the horizontal direction:

High resolution P3-P3mx system image

Terms for use: There are no restrictions on the use of these images. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to dow[at]uoregon.edu, and credit are appreciated but not required.