Informal Geometry
Lab #19
Fractals II
Name_____________________
Partners Names___________________
Definition: A figure is
selfsimilar
if parts of the figure are small replicas of the whole figure.
Definition: A
fractal
is a selfsimilar figure.
Definition: A figure is
strictly selfsimilar
if any arbitrary part of the figure contains an exact
replica of the whole figure.
Definition: The
box count
of a figure is the number of boxes in a grid with at least a small
portion of the figure in it.
Definition: The
box dimension
of a figure is the slope of the bestfitting line for the points
(log
10
(x), log
10
(y)) where x is the total number of boxes in the box count grid and y is the box
count of the figure.
Definition: The
similarity dimension
of a selfsimilar fractal shape from line segments is
log (
)
log ( )
10
10
N
r
, where N is the number of smaller line segments replacing a larger segment at each
iteration, and r is the amount any segment is longer than each of the segments at the next stage.
Definition: The
fractal dimension
of a strictly selfsimilar fractal is the limit of the box
dimension as n approaches infinity, which also equals the similarity dimension.
So fractals frequently have fractal dimension that is not an integer.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Dechene
 Geometry, Fractal, Koch snowflake, Koch curve

Click to edit the document details