Fractals can be chaotic-having the charactersitic of sensitivity to change in intital conditions.
Here are two examples of chaos.The first,a plain vanilla Mandelbrot zoom,
has the chaotic nature of the artificial.The pattern while convoluted and serpentine
is not noisy-it does not have randomness it because it is strongly self-similar.For example it is  perfectly symmetrical.
The second mimics natural chaos-it is superficially random. There is the hint of structure
in the discernible spiral but it has the irregular variations of the natural world.
Unending complexity from the simplest of algorithms. 
fract020.gif       { ; A mainstream minibrot
                     ; blank
                     ; calctime   0:00:54.72
                     ; created Apr 08, 2010
                     ;  Fractint Version 2004 Patchlevel 9
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  }
fract279.gif       { ;Organic or inorganic?
                     ; blank
                     ; blank
                     ; created Apr 08, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=*.frm formulaname=H05-17
  function=sin/sqr
  center-mag=-1.30971817008782600/+1.06416508897457400/136.5077
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frm:H05-17 {; V.1.1 - earlier versions may be discarded
        ; Copyright (c)1998,1999 Morgan L. Owens
        ; = 2(xH(4)-4H(3))
  z=pixel, oz=0
  fz=0
  zt=fn1(z)+p1:
  foz=fz
  zz=z*z
  fz=8*z*(4*zz*(zz-5)-9)
  z=z-p2*fz*(z-oz)/(fz-foz)
  oz=zt
  zt=fn2(z)
  |fz|>=0.0001
  ;SOURCE: chby17.frm
}

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