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13 Articles that combine these categories:

`Categories`

fractal + logo(See also: all categories, featured categories, featured articles, all articles. Sort articles by name, created, edited)

13 Articles that combine these categories:

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…

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…

Perhaps the best known Space Filling Curve is the Hilbert Curve. to hilbert :count :size :angle if :count > 0 [ rt 90*:angle hilbert (:count - 1) :size (:angle * (0-1) ) fd :size rt 90*:angle * (0-1) hilbert (:count - 1) :size :angle fd :size hilbert (:count - 1) :size :…

A Koch curve is a well-known fractal, first described by a Swedish Mathematician, Helge Von Koch, in his paper "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire". Put three Koch curves together in a triangular configuration and you have…

In the article on Koch Curves we derived the famous koch-curve, by starting with a line, then a bumpy-line, then a self-similar recursive bumpy-line. The final result looked like this: to koch_curve :length :limit ifelse :limit = 0 [ fw :length ] [ koch_curve :length/3 :limit -…

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…

to half_sierpinski :size :level ifelse :level = 0 [ forward :size ] [ half_sierpinski :size :level - 1 left 45 forward :size * sqrt 2 left 45 half_sierpinski :size :level - 1 right 90 forward :size right 90 half_sierpinski :size :level - 1 left 45 forward :size * …

A Sierpinski triangle is the result of this line of thinking: To draw a Sierpinski triangle just draw three smaller Sierpinski triangles. (Unless the shape is too small... then just draw a regular triangle). What if we make the number 3 a parameter, :side, so that we create Sie…

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…