23966k - Instituto Carlos I - Universidad de Granada

FIGURE 3. This (ζ ,ξ ) projection of the doubly-thermostated oscillator fractal is shown at five successive
stages of temporal resolution. The time intervals between successive points range from 0.001, the
Runge-Kutta timestep, to 10.0, showing how a continuous trajectory can lead to a fractal object.
FIGURE 4. Sierpinski Sponge, constructed by removing 7 of the 27 equal cubes contained in the unit
cube, leaving 20 smaller cubes, and then iterating this process ad infinitum leaving a 2.727-dimensional
fractal of zero volume.
largest cube the density vanishes. Unlike the multifractal of Figure 3, the Sierpinski
sponge is homogeneous, so that an n-fold enlarged view of a small part of the sponge,
with an overall volume 1/27 n of the total, looks precisely like the entire object.