Pythagorean Tree with L-System?

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Postby Ailurus » Sat Oct 23, 2010 12:17 am

Hi,

I wondered whether it is possible to create a Pythagorean tree using the L-System (=Lindenmayer System) function. With the help of Tavmjong's book I succeeded in creating a Koch's snowflake, after I couldn't find out how to create one myself (only got one side working).

Next challenge: a Pythagorean Tree.
Info: http://mathworld.wolfram.com/PythagorasTree.html

(Click for full size)


I cannot figure out how to make lines of different lengths (the F-lines should be A/sqrt(2) long). Moreover, when I increase the order, it doesn't work as I thought it would be.
Is it possible?

PS: Found this on Flickr, should be possible? http://www.flickr.com/photos/botond-balazs/3596225404/

Re: Pythagorean Tree with L-System?

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Postby brynn » Sun Oct 24, 2010 11:46 am

I cannot figure out how to make lines of different lengths (the F-lines should be A/sqrt(2) long).

This is mostly way over my head. But after 15 minutes playing around with the L-System dialog, it looks to me like parameters are needed for pyth. tree, which are not available in the dialog. However, strong emphasis on "way" over my head!
Good luck

Re: Pythagorean Tree with L-System?

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Postby Ailurus » Sun Oct 24, 2010 11:02 pm

Hey Brynn,

Thanks for your time anyway . I spend some more time on it, and got a little bit further:



The Axiom and Rules are OK now, but I need some scaling. I edited the scripts and added a box "Factor", and typed the value of sqrt(2)/2. However, I'm not sure how to scale the lines. At first I thought each "level" would be drawn individually, that would make it easy to pass a level parameter to the drawing function. However, first the entire thing is "calculated" (see MessageBox).
Hm, I think this question is becoming a Python related question

Re: Pythagorean Tree with L-System?

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Postby Ailurus » Mon Oct 25, 2010 12:06 am

Ok, I solved it for now in a dirty way (it is only applicable for Pythagoras Trees which use the exact syntax as in the image below). Click for a larger version.



The B in the rules replaces the F in the old one. Why? Because B shouldn't scale like the other lines. In other words, B is a line at the previous level. The other variables (A and F) should scale with sqrt(2)/2 per level.

I added this line to lindenmayer.inx:

Code: Select all

<param name="factor" type="float" precision="8" min="0.0" max="100.0" _gui-text="Factor">0.0</param>

To the file lindenmayer.py I made some more changes. Most important ones, In the __recurse() part:

Code: Select all

addition = self.__recurse(self.rules[c],level+1)

                    addition = addition.replace('A','A*')
                    addition = addition.replace('B','B*')
                    addition = addition.replace('F','F*')
                   
                    level_string = level_string + addition

This adds an asterisk after each occurrence of A, B and F. So at level 0, there won't be any asterisks, the lines at level 1 will have one, etc. Next, the __compose_path():

Code: Select all

i = 0
        while i < len(string):
            if string[i] in 'ABCDEF':
                self.turtle.pd()
                scaling = 0
                while (i+1+scaling < len(string) and string[i+1+scaling]=='*'):
                    scaling+=1
                   
                if string[i] == 'B': #Scale with respect to the previous level, so decrease scaling.
                    scaling-=1
                   
                self.turtle.fd(self.options.step * (self.options.factor**(scaling)) * (random.normalvariate(1.0, 0.01 * self.options.randomizestep)))

This counts the amount of asterisks after the A, B and F characters. Since B should scale with respect to the previous level, there is an extra if-clause. The actual scaling happens by multiplying the step with the factor^level.

Since I'm not familiar with Python, there may be more elegant solutions .

Re: Pythagorean Tree with L-System?

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Postby Ailurus » Mon Oct 25, 2010 1:28 am

Oh, one other thing. It is of course also possible to use the factor with other fractals, for instance Koch's Snowflake. When setting the factor to 1/3, the size of the figure stays the same, instead of growing with a factor 3 (like in the original version) each level


Once again, click for the larger version.

Re: Pythagorean Tree with L-System?

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Postby brynn » Mon Oct 25, 2010 3:47 am

I edited the scripts and added a box "Factor"....

Wow! You are way above me, being able to write the code, lol. Perhaps you might like to collaborate with the author of that extension, to produce a new extension, possibly for inclusion in a future release? In any case, I would love to have such. I quite enjoy working with fractals, and I think some quite impressive images could be created with your script/extension. I have played with L-System extension in the past, but never got very far, for exactly the reason you found. So this would really be a very nice tool for everyone. (I can think of one Inkscape user in particular, who like me, has a passion for fractals, and there are probably many more.)

Well, congratulations on some fine work

Re: Pythagorean Tree with L-System?

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Postby Ailurus » Tue Jul 17, 2012 5:44 am

Wow, this topic is even older than I thought.

Anyway, recently I started working with L-systems again, and implemented something in MATLAB. When I have enough time, and know more about coding extensions for Inkscape (is there a tutorial somewhere?), then I would like to update/rewrite the L-system extension, such that you can also create things like this.



I tried to upload the SVG file, but it's about 4.4 MB . So I included the PDF file (on A3 format), if you want you can create an SVG from that file.

Attachments

PythTree_A3Format.pdf

(88.28 KiB) Downloaded 349 times

Re: Pythagorean Tree with L-System?

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Postby brynn » Tue Jul 17, 2012 4:45 pm

Wow, impressive!

There aren't any tutorials that I know of, for writing Inkscape extensions. Although we get more requests than ever, these days. I usually direct people to the Developer's section of the Inkscape wiki, as a starting place. Also, in this forum's Programming subforum, a member named LiquidAsh has written somewhat of a guide, but it's not directly about writing extensions. I don't understand much about programming, so I can't explain it very well.

I played around with that L-system extension, since my last reply in this topic. I managed to make some interesting stuff, and actually to understand it a little better. It's really hard to figure out how to make a particular shape, and especially without the lines overlapping each other a bazillion times (resulting in huge files). It's a very complex extension