# Category: fractal

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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)

# Articles...

### Dragon Curve

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…

### Fern Fractal

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…

### FlowSnake

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 the…

### Fractal

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)…

### Harriss Spiral

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…

### Sierpinski Carpet

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 warn…

### Sierpinski Triangle

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 f…

### Space Filling Curves

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…

### Tree Fractal

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 …

### Unbounded Recursion

Please see Unbounded Recursion (Alternatively see Recursion where you can learn about applying bounds to your recursion, or detecting cycles in referential data structures) there is no general method to determine whether a given program will ever halt or will run forever; this is…

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