The purpose of this project is to randomly generate a 2D fractal landscape and create a 3D projected image of the landscape. To implement this, we used the Diamond-Square Algorithm, which is commonly ...

Due to their previously discovered fractal nature, financial data patterns are self-similar when scaling up. New research shows that the most extreme events in financial data dynamics-reflected in ...

ABSTRACT A fractal landscape realizer has been developed that generates synthetic landscape maps to user specifications. The alternative landscape realizations are not identical to the actual maps ...

We live in a world of three-dimensional objects bounded by two-dimensional surfaces and outlined by one-dimensional lines. All in all, a comforting, intelligible, whole-number sort of world. Or do we?

Realistic landscapes can be generated with the midpoint displacement algorithm (see Section 9.6 in PJS). In one type, one begins with a flat square grid and an arbitrary (positive) displacement of the ...

Due to their previously discovered fractal nature, financial data patterns are self-similar when scaling up. New research shows that the most extreme events in financial data dynamics—reflected in ...

These images show the effect of changing the scaling parameter. At each stage in the construction, a random displacement of the midpoints is made according to the formula avg + scale*rand where avg is ...