Be careful about the concept of fractals in scaling designs from small to
large.

Cube-square scaling is an instance: this is where a 'design' depends upon
two things that scale in different ways. In the 'resultant' scaling relation
expressed as a power of the scaling factor, the power is the "fractal
dimension". For example, in condensation theory the size of droplets depends
on competition between the weight of the droplet (a volume term, length
cubed) and the surface tension/surface energy that holds a droplet together
(an area term, length squared), so that there is a 'best size'. Another
example is Brunel's success in getting his first ship (the Great Western
paddle steamer) from Bristol to New York with coal to spare. Critics has
said it would run out of coal but Brunel realised that the resistance to the
ship going through the water depended on the wetted area of the hull whereas
the amount of coal the ship could carry depended on the height of the hull
(an extra dimension). 

The best example of this sort of thing as it relates to design is anything
that will break. The energy required for cracking is an area term: energy
stored or dissipated is a volume term. This is why large structures made
from bodies which appear to be ductile in laboratory-sized testpieces can
break in a brittle fashion, and why large energy-absorbing devices do not
live up to expectations when extrapolated from small 'models'. Again, going
the other way, it is why powders cannot be ground up below certain minimum
sizes.

In all these cases the fractal dimension itself depends upon size.

Anyone still awake may wish to look at Jim Gordon's books and also at Chap 9
on scaling in my book with Mai Yiu-Wing 'Elastic and Plastic Fracture' Ellis
Horwood/John Wiley 1985/88. There are also later papers to which I could
refer people.

Tony




> there is an approach to use fractal geometry in connection with urban
> planning and settlement (the
> borders of cities and the patterns of urban strucures in general)
> information can be found in "prozess und form natürlicher konstruktionen",
> esp one article of humpert,
> becker and brenner on the development of urban agglomeration
> 
> petra
> 
> -- 
> 
> univ.ass. dipl.ing. petra gruber
> tel +43-1-58801-27022 _ fax +43-1-58801-27092
> [log in to unmask] _ www.hb2.tuwien.ac.at
> 
> department of design and building construction E 253/5, prof. helmut
richter
> institute for architecture and design, tu-vienna, karlsplatz 13, A-1040
> vienna, austria
> 
from Prof Tony Atkins ScD FREng
School of Construction Management and Engineering
Engineering Bldg
University of Reading
READING RG6 6AY
Tel +44 118 931 8562
Fax +44 118 931 3327