Talk:L-system

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This paragraph is unclear to me:

As an L-system these tilings are called Penrose's rhombuses and Penrose's tiles. Above pictures were generated for n=6 as an L-system. If we properly superimpose Penrose tiles as an L-system we get next tiling:

It doesn't define what n is. It doesn't define what "properly superimpose as an L-system" means. It doesn't say which L-system was used to generate those images. I can't guess these from context. --LC

in the canter dust example,it contains a line of "constant" about some 60 degrees. what's that line doing there? I think it is wrong.

in the Koch snowflake example, shouldn't the plus and minus sign be part of the alphabet?

i think the penrose tiling example is a bit forced. Penrose tilings are aperiodic. So, i doubt it can be reduced to a string replacement system.

also, i'm not sure L-Sytem has a place in serious math. If it does, it is or relates to formal logic. Should there be a mention?

thanks.

Xah P0lyglut 11:18, 2004 Jan 15 (UTC)

Contents

[edit] Constants?

In Example 3, Cantor Dust, what are the constants for? (I'm not even sure if that's one, two, or three constants you're trying to list.) You never seem to use them.

Concerning the Koch curve shouldn't + and - be constants (clearly there're no productions for them). According to the definition stated, the alphabet consists of variables, hence I disagree with the poster asking that they should be included in the alphabet.


[edit] Koch curve

I would like to see one higher order iteration (n=20 ?) of the Koch curve. IMO, the result is illustrative and pretty impressive especially for people new to the subject.

[edit] Need new Penrose time images

The three images of Penrose tilings are all untagged, and they don't have authorship info (dating from before "the big conversion"). I guess when the next untagged-image jihad gets underway these images may well meet with infinite justice, so we need to start thinking about replacements for them ASAP. It's a bummer, as they're really attractive images. -- Finlay McWalter | Talk 15:17, 7 October 2005 (UTC)

These images were made by me with Winfract version 18.21, and we can tag them as public domain. I'll do that right the way. --xJaM 14:02, 21 October 2005 (UTC)

[edit] Example 1 seems strange to me

Lindenmayer's original L-system for modelling the growth of algae.

variables : A B
constants : none
start  : A
rules  : (A → AB), (B → A)

which produces:

n=0 : A → AB
n=1 : AB → ABA
n=2 : ABA → ABAAB
n=3 : ABAAB → ABAABABA

I would expect it to look like this more in keeping with how the others are shown:

n=0 : A
n=1 : AB
n=2 : ABA
n=3 : ABAAB
n=4 : ABAABABA

Am I missing something? Hogan 02:11, 29 April 2006 (UTC)

Yes, you are right - the format of Example 1 was not consistent with the format of other examples. I have fixed it. Gandalf61 08:16, 2 May 2006 (UTC)

[edit] Another example: Heighway dragon

Another nice example is a dragon curve. It is described by the following L-system:

variables : L R
constants : + −
start  : R
rules  : (R → R+L), (L → R−L)

meaning, respectively:

L, R — step forward
plus — turn right by 90°
minus — turn left by 90°

Some initial strigns are:

n=0 : R
n=1 : R+L
n=2 : R+L+R−L
n=3 : R+L+R−L+R+L−R−L
n=4 : R+L+R−L+R+L−R−L+R+L+R−L−R+L−R−L

CiaPan 20:53, 6 October 2006 (UTC)

[edit] Merge with graftal article?

I've added graftal to the "See Also" section, but does it really need a separate article? There doesn't seem to be a whole lot of difference between L-systems and graftals. Perhaps the articles should be merged together. What do you think? -- Sakurambo 桜ん坊 13:53, 15 May 2007 (UTC)

[edit] Better examples

Some of the examples given in this article are a bit rubbish. The first example provides no explanation of what is going on. What does the string "ABAABABAABAABABAABABAABAABABAABAAB" have to do with algae? If the only important information is the length of each sequence, then how does this differ from Fibonacci's modelling of rabbit populations? The second example is completely redundant — the first example also generates a Fibonacci sequence, in case you hadn't noticed, and in any case, there's a much simpler algorithm for calculating this series, so in what way is this a useful example of the capabilities of an L-system? Examples 5 and 9 are quite useless without the rules used to produce these figures. -- Sakurambo 桜ん坊 14:10, 15 May 2007 (UTC)