- What Do You Think?
Q2.15: What does it mean to you that an object has a fractional
dimension? (HINT: The following questions could prompt their thinking:
How does the object fill space? Is its use of space dense or sparse?
Are its edges smooth or jagged? What is similar throughout different
parts of the object? What is random or different throughout different
parts of the object? How does the whole object compare with individual
parts of the object? What geometric shapes do you see in the object:
circles, lines, ovals, spheres?)
Q2.16: Is there a quantitative difference between measuring
the coastline by the "ruler method'', "box method'',
and "circle method''? If so, can you explain why? Why
would scientists need all three methods (i.e., why don't they
just pick the "best one'')? HINT: Think of some examples
from nature which would be better suited towards a particular
Q2.17: In the beginning of this unit, we talked about the length
of the coastline as measured by various observers (e.g., an automobile,
bicyclist, jogger and bird). Can you say whether the fractal dimension
of the coastline measured by these observers would be the same
or different? How does it change (or not change)? Which observer
would get the most accurate fractal dimension?
2.4 - Dimensions and Logarithms