<s>
Analysis	B-Algorithm
on	I-Algorithm
fractals	I-Algorithm
or	O
calculus	B-Algorithm
on	I-Algorithm
fractals	I-Algorithm
is	O
a	O
generalization	O
of	O
calculus	O
on	O
smooth	O
manifolds	O
to	O
calculus	B-Algorithm
on	I-Algorithm
fractals	I-Algorithm
.	O
</s>
<s>
The	O
theory	O
describes	O
dynamical	O
phenomena	O
which	O
occur	O
on	O
objects	O
modelled	O
by	O
fractals	B-Application
.	O
</s>
<s>
It	O
studies	O
questions	O
such	O
as	O
"	O
how	O
does	O
heat	O
diffuse	O
in	O
a	O
fractal	B-Application
?	O
"	O
</s>
<s>
and	O
"	O
How	O
does	O
a	O
fractal	B-Application
vibrate	O
?	O
"	O
</s>
<s>
In	O
the	O
smooth	O
case	O
the	O
operator	O
that	O
occurs	O
most	O
often	O
in	O
the	O
equations	O
modelling	O
these	O
questions	O
is	O
the	O
Laplacian	O
,	O
so	O
the	O
starting	O
point	O
for	O
the	O
theory	O
of	O
analysis	B-Algorithm
on	I-Algorithm
fractals	I-Algorithm
is	O
to	O
define	O
a	O
Laplacian	O
on	O
fractals	B-Application
.	O
</s>
