"Sierpinski Valentine" Discussion

[leveldeaded]

I guess that means we iphone users are mediocre[/tear]

Don't feel bad. You're not alone. Opera Mobile on my WinMo phone won't display it either. People who use Firefox prior to version 3 only see a truncated version of the title text, IIRC.

You can see the title text on your iPhone (as well as create a printable version on your computer) if you use my printifier.com

You can just look at the Comic Thread instead of the comic itself on your iphone, and get the mouseover text printed out nicely for you. See how much I trust my Comic thread forum?

[feldgendler]

One day,
A mad meta-poet
With nothing to say
Wrote a mad meta-poem
That started: “One day,
A mad meta-poet
With nothing to say
Wrote a mad meta-poem
That started: “One day,
[...]
sort of close”,
Were the words that the poet
Finally chose
To bring his mad poem
To some sort of close”,
Were the words that the poet
Finally chose
To bring his mad poem
To some sort of close”.


I hope it's obvious how this is relevant to the topic.

[orbus]

Orbus & mezz, your renderings are stunningly beautiful.

Thanks! Having other people enjoy it really justifies the time I spent hacking mine together. =) (And I agree, Mezz's is really cool, too - it reminds me of something out of Psychonauts, especially in that color scheme.)

Speaking of hacking it together, there's a bug in the earlier version - I'd messed up, which is why hearts in the upper portion of the fractal that were off the center-line looked less heart-y and more blob-y.

It's a few lines of code, and one new rule added to tune the positioning, and now all the hearts look like hearts. =)

Code: Select all

    startshape OuterTriad

    rule RedSquare {
       SQUARE {hue 0 sat 1 b 1 alpha -0.95}
    }

    rule OuterTriad {
       RedSquare{}
       OuterIndentTriad {s 0.5 x 0.25 y -0.25 flip 90}
       OuterIndentTriad {s 0.5 x -0.25 y -0.25}
       Triad {s 0.5 y 0.25}
    }

    rule Triad {
       RedSquare{}
       SkewTriad {s 0.5 x 0.25 y -0.25 flip 90}
       SkewTriad {s 0.5 x -0.25 y -0.25}
       Triad {s 0.5 y 0.25}
    }

    rule SkewTriad {
       RedSquare{}
       LowerBentIndentTriad {s 0.5 x 0.25 y -0.25}
       BentTriad {s 0.5 x -0.25 y -0.25}
       UpperIndentTriadB {s 0.5 y 0.25}
    }
       
    rule BentTriad {
       RedSquare{}
       SkewTriad {
          size 1 (1 / (1 +( tan (25) / 2)))
          y ((tan (25) / 4) -.023)
          skew 0 25
       }
    }

    rule OuterIndentTriad {
       RedSquare{}
       LowerOuterIndentTriad {s 0.5 x 0.25 y -0.25}
       OuterIndentTriad {s 0.5 x -0.25 y -0.25}
       UpperIndentTriad {s 0.5 y 0.25}
    }

    rule LowerOuterIndentTriad {
       RedSquare{}
       OuterIndentTriad {
          x (- tan(15) / 2)
          size 1
          skew -15 0
       }
    }

    rule UpperIndentTriad {
       RedSquare{}
       Triad {
          skew 10 0
          size .74 1
          x -.07
       }
    }

    rule UpperIndentTriadB {
       RedSquare{}
       Triad {
          skew 8 0
          size .78 1
          x -.05
       }
    }

    rule LowerBentIndentTriad {
       RedSquare{}
       BentTriad {
          x (- tan(15) / 2 +.055)
          size 0.91 1
          skew -15 0
          flip 90
       }
    }

    rule UpperIndentSkewTriad {
       RedSquare{}
       SkewTriad {
          skew 8 0
          size .8 1
          x -.05
       }
    }

Contractually Obligated Link to Flickr

[mezz]

Orbus & mezz, your renderings are stunningly beautiful.

Thank you I'm glad you liked it.

The linked picture looks vaguely Giger-esque.

I also have a nicer heart fractal I made a long time ago:
http://img.photobucket.com/albums/v33/m ... y-copy.jpg

Hmm, that's really quite good. May I ask how it was formed?

I made it using apophysis.
Most people find the learning curve a bit daunting, but it's fun.

Here is how the basic heart is made:
make a new flame, set the first transform to linear = 0, blur = 1,
make a final transform of linear = 0, julianscope = 1,
move the final transform up and to the right.

Or just open up the program and ctrl-v the following into it (there's no specific place to paste, it will accept it anywhere):

Code: Select all

<flame name="heart" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
   <xform weight="0.5" color="0" blur="1" coefs="1 0 0 1 0 0" />
   <finalxform color="0" symmetry="1" juliascope="1" coefs="1 0 0 1 0.18 -0.7" juliascope_power="2" juliascope_dist="1" />
   <palette count="1" format="RGB">FF69B4</palette>
</flame>
</Flames>

That's the start. Just build up from there
There's a hole in the center, but I just photoshopped it.

[sableye22]

One day,
A mad meta-poet
With nothing to say
Wrote a mad meta-poem
That started: “One day,
A mad meta-poet
With nothing to say
Wrote a mad meta-poem
That started: “One day,
[...]
sort of close”,
Were the words that the poet
Finally chose
To bring his mad poem
To some sort of close”,
Were the words that the poet
Finally chose
To bring his mad poem
To some sort of close”.


I hope it's obvious how this is relevant to the topic.

I get it. Ha.

[FatPhil]

I must say that I do like the very different approaches people have used to generate mathematically-modelled, rather than simply artistic, fractals.

My post count is zero currently, so won't post a link to my own humble offering quite yet, but if you are impatient and have the nouse to track my website down, there's a directory called images on my website and a file called heart7.png . Of course, a real link will follow as soon as I can meaningfully contribute to a few more threads. Good work all - in particular the orinal and artistic best!

And the real link would be this:

[aterimperator]

Is that a love triangle?

Ha, I missed this the first time through...


Anyway, I was thinking about this problem, and would one good approach be that of a sort of "canonball problem"? I.e. what you have is a triangle, and the problem is how to most effectively remove all area via cardiods? This could solve the warping problem, though it might result in something looking a lot less like a Sierpinski fractal.

[orbus]

One day...

I really don't see why you felt the need to elide the middle portion of your poem! Surely we're all mature adults, there's no need for censorship here!

Here, I've taken the liberty of typesetting the whole thing for you and re-posting it.


Larger Version

In all seriousness, thanks to feldgendler for posting the poem, and to Douglas Hofstadter for originally suggesting this method of textual abuse. Very simply, each sub-iteration of the poem is printed at 2/3 the size of the parent, which rapidly trends to pixel-dust - though, if we had infinite resolution, there's no reason not to have "poems all the way down," to steal a phrase.

If you want the source, just ask - I'm not posting it because it's terribly long and tedious. The "fractal source" - the heart of the trick - is about three lines of elegance, while convincing Context Free to render letterforms and words is about a thousand lines of kludgy library. (It is, however, reusable, so if anyone besides me wants to abuse CFDG for producing text, I'll happily share it and save having to duplicate the effort.)

[tunah]

(click for full)

I wrote some code that uses the borders of the heart to deform triangular meshes that describe the shape of each of the corner sections of the gasket. You can translate a point on the triangular gasket to the equivalent point on the heart-shaped one by finding the corner it lies in, recursively finding its position within that gasket, and then transforming it using the mesh.

Then the actual shape was drawn with the random walk.

The functions wrapped around the triangle were
y = -R/2 + √(R^2 - (|x-0.5| - R)^2)
and
y = x tan (2A - π/6), x≤0.72046,
y = 1+√3/2 + √(R^2 - (x + √3 - 5/2)), x>0.72046

[thenotestaken]

What an awesome thread! Valentines are a great use of coding/math skills, though I have to ask--did any of you actually use these for a special someone?

[feldgendler]

orbus: the poem indeed makes a much stronger impression without omissions! Thanks for publishing your typesetting excercise.

BTW, credits for the poem itself go to an anonymous author. I saw it from UNIX fortune.

[Marleen]

I'm impressed.

I love the meta-poem.

I love the new Sierpinski hearts.

[dennisw]

I'm impressed.

I love the meta-poem.

I love the new Sierpinski hearts.

boom-de-yada

[Faranya]

Aww, my valentine was nothing as great as this one though...

All it had was a set of labeled axis and a piecewise function of two quadratics and an absolute function into the shape of a heart...

Oh well, maybe next year...

[tahrey]

Loli haet valentines day

But I love these fractals, they give the requisite warm fuzzy feeling.

And make me feel like it's 1995 all over again.

[martin878]

I made it using apophysis.
Most people find the learning curve a bit daunting, but it's fun.

I agree. You inspired me to start playing with it:

Spoiler:

Fractal flame that looks like a plant

Apophysis-090223-202.jpg (99.21 KiB) Viewed 732 times

[aterimperator]

I made it using apophysis.
Most people find the learning curve a bit daunting, but it's fun.

I agree. You inspired me to start playing with it:

Needs to be brighter further away from the edges.

[xdaemanix]

aw not going on the internet for a few weeks sucked.... im late... but the rollover text made me ^.^