# Category: chaos

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The Dragon Curve or Dragon Fractal is a nifty little shape! Here are the first 12 iterations. You see the dragon shape begin to emerge. I've put a red dot before each one, so you can see how it doesn't always go forward right away. ;export dragon to dragon :count :length :angle…

A simple self-similar fractal. Similar to a Tree — in particular it's very similar to the Pine, but with a tilt before drawing the next segment. to fern :segment :curve :angle1 :angle2 :ratiobranch :ratiostem :limit penwidth :segment/4 ifelse :segment>:limit [ color [60 40 20] r…

The flowsnake, also known as the 'Peano-Gosper' curve is a rather dashing space-filling curve. There is also a demonstration of it on the space-filling curves page. The following implementation uses 'mutual recursion' - i.e. two methods that call each other. The flowsnake has t…

Fractals are mathematical sets that exhibit self-similarity at different scales. Why are they called 'Fractals'? Because they are not exactly two dimensional (or three dimensional or four dimensional or one dimensional) they have a 'fractional dimension' (like 2.5)…

Few spirals are as beautiful as the Harriss spiral. to curve :length pu lt 45 fd :length/2 * sqrt(2) rt 90 pd penwidth :length/15 arc :length/2 * sqrt(2) 90 pu fd :length/2 * sqrt(2) lt 90 lt 45 rt 90 pd end to harriss :length :limit if :length > :limit [ color [200…

A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling ... - Wikipedia: Penrose tiling Yeh yeh yeh we know all that. APERIODIC No repeating period. Get this -- it's true chaos.…

This page is an example of bound recursion. If you've already read this page, please stop reading now. Otherwise, please continue. To be useful, recursion needs to have boundary conditions, base cases, exits, limitations: things that stop it from running on forever and ever and…

Sierpinski didn't just mess around with triangles, he also wrote 50 books (all of them flip-books of Sierpinski triangles, I assume), created a curve and finally — the highlight of his storied career — he released this: his Sierpinski Signature Edition Carpet design. A short war…

Anything that's covered here is almost definitely covered in a very well known webpage, The Sierspinski Triangle Page to End Most Sierspinski Triangle Pages but regardless, I must press on. Let's draw a triangle. to triangle :length fd :length lt 120 fd :length lt 120 fd :…

Space-filling curves! Amazing things. Peano sat around thinking and thinking, What was he thinking? He was thinking: I wonder, I wonder, I wonder! Can I draw a continuous line that touches every single point of the unit square, exactly once? (i.e. it never crosses itself!) No…

A simple self-similar fractal. Similar to a Fern Here's one that bifurcates at every iteration. By altering the angle of the branches we get completely different shapes. Topologically identical, but visually very different. ;export tree to tree :length :branches :angle :ratio …

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