Fractals

From GenerativeArt

(Difference between revisions)
Jump to: navigation, search
(→Fractal or Box Counting dimension: Added content)
Current revision (22:33, 16 September 2013) (view source)
(→Fractal or Box Counting Dimension)
 
=====Stochastic fractal river=====
=====Stochastic fractal river=====
Both fractals and L-systems can have stochastic (random/chance) forms.
Both fractals and L-systems can have stochastic (random/chance) forms.
-
   '''function''' RIVERBEND(x1, y1, x2, y2, res)
+
   //  Given:
 +
  //  res                      :length of smallest line to be drawn
 +
  //  DIST(x1, y1, x2, y2)    :distance between points (x1, y1) and (x2, y2)
 +
  //  BEND(x1, y1, x2, y2)    :returns x3,y3 randomly between and offset
 +
  <br>
 +
'''function''' RIVERBEND(x1, y1, x2, y2, res)
       '''if''' DIST(x1, y1, x2, y2) > res
       '''if''' DIST(x1, y1, x2, y2) > res
-
           // pick a random point on the line
+
           BEND(x1, y1, x2, y2)
-
          // offset it by a random amount
+
-
          // that new point is (x3, y3)
+
           RIVERBEND(x1, y1, x3, y3)
           RIVERBEND(x1, y1, x3, y3)
           RIVERBEND(x3, y3, x2, y2)
           RIVERBEND(x3, y3, x2, y2)
{{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/fractImg3.gif|caption=Note that a line segment has a fractal dimension of 1}}<br />
{{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/fractImg3.gif|caption=Note that a line segment has a fractal dimension of 1}}<br />
{{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/fractImg4.gif|caption=Note that a square has a fractal dimension of 2}}<br />
{{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/fractImg4.gif|caption=Note that a square has a fractal dimension of 2}}<br />
-
{{SingleImage|imageWidthPlusTen=510|imageURL=http://philipgalanter.com/generative_art/graphics/box_counting_dimension.png|caption=Here is an illustration of the box counting method to measure the fractal dimension of actual objects}}<br />
+
{{SingleImage|imageWidthPlusTen=600|imageURL=http://philipgalanter.com/generative_art/graphics/sierp-det.GIF|caption=The Sierpinski triangle is constructed yielding 3 copies at 1/2 size so the fractal dimension = log(3)/log(2) = 1.58}}<br />{{SingleImage|imageWidthPlusTen=1000|imageURL=http://philipgalanter.com/generative_art/graphics/box_counting_dimension.png|caption=Here is an illustration of the box counting method to measure the fractal dimension of actual objects, in this case the coastline of England}}<br />

Current revision

Retrieved from "http://philipgalanter.com/generative_art/wiki/index.php5?title=Fractals"
Personal tools