### word | form:

Fractal
* All fractals are members of a complex and infinite family tree
  - contain the element of self-similarity
* Most fractals also have an infinite perimeter and a finite area
  - are just a graph of an equation using complex numbers
* also give rise to examples of nowhere differentiable curves
  - have technological applications
* are a different kind of image
  - fairly new concept in math and geometry, and quite different than the norm
  - geometric application of recursion
  - geometry of shapes which are equally rough at all scales
  - good example of convergent infinite processes
  - serendipitous art
  - subclass of shape grammars
  - visual expression of the dynamics of chaos
  - actually a mathematical concept
  - an example of a part of nature and science that are often considered artistic
  - anything that contain self-similar images within itself
  - art created with the use of mathematical formulas
  - beautiful computer-generated images made using chaos theory
* are complex and recursive mathematical images that are really neat to view
  - geometric shapes that commonly exhibit the property of self-similarity
  - objects with self-similarity, which are created using some fixed algorithm
  - complex, detailed geometric patterns found throughout the natural world
* are computer generated graphics based on mathematical equations
  - images generated by iteration of equations
  - different from other geometric figures because of the way in which they scale
  - distinct from the simple figures of classical, or Euclidean , geometry
  - educational because they illustrate many basic mathematical functions
  - evident in the works of all artists
  - excellent at creating realistic images, because they can model natural objects well
  - geometric shapes which repeat on an ever diminishing scale
  - graphic representations of some of the principles of the science of chaos
  - graphs and they are graphic art
* are highly complicated and irregular geometric objects
  - itterative
  - images created by using mathematical formulas and complex mathematics
* are infinitely complex computer art
  - self-similar , iterated mathematical constructs having fractal dimension
  - intricate patterns repeating at different size scales
  - mathematical functions of complex variables
* are mathematical objects that can be drawn by a computer
  - with strange properties
* are mathematical representations of arbitrarily complex objects
  - repititive elements of compound events or objects
  - structures, which on an ever smaller scale infinitely repeat themselves
  - mathematically based pictures which appear very complex and sometimes beautiful
  - mathematics on display
  - more or less related to chaos theory, complexitytheory
  - part of the mathematics of chaotic systems
* are pictures designed by a mathematical formula
  - that visualize the behavior of various mathematical equations
  - sacred mandalas in the new millenium
  - self repetitve images, looping within themselves infinitely
  - self-similar structures
  - sets of complex geometric shapes that look the same over a wide range of scales
  - shapes that repeat themselves on different scales within the same object
  - similar structures - they demonstrate their similarity at different scale levels
  - simple pictures that visualize the behavior of various mathematical equations
  - simple, nonlinear systems with complex dynamical properties
* are the beauty pageant of mathematics
  - first schizophrenic styling products using optical brighteners
  - geometry of nature
  - place where math, science and art come together
  - second essential characteristic of chaos
  - very beautiful geometric figures that can be used to describe nature
  - visual representations of mathematical formulas
* arise in the context of the behaviour of iterative systems.
* can also occur in the real world.
* can be anything that contains self-similar images within itself
  - either regular or irregulas
  - have fractional dimension
* do appear to exist and the patterns the plants display seem never ending.
* exhibit different kinds of self-similarity.
* exist natively as electronic images.
  - borders between self and world
* get their name because they can be seen to have fractional dimension.
* have fractional dimensions
  - many interesting applications, including image compression
* hold infinite spin and information and awareness density in their heart.
* imply nonlinearity in the process which created the fractal process.
* make it possible to understand chaotic behavior - infinity within finite boundaries
  - the shapes seen in nature
* often look like objects in nature.
* play a key role in dynamical systems.
* show up in everything from cumulus clouds to leaves on trees.
* signify non-Euclidean or fractional Euclidean geometrical structure.
* turn out to be one way to measure chaotic systems.
+ Fractal, Uses
  * Some fractals exist only for artistic reasons, but others are very useful. Fractals are very efficient shapes for radio antennas and are used in computer chips to efficiently connect all the components. Also, coastlines can be thought of as fractals.