Filling a Square with Random Disks

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A unit square is filled randomly with non-overlapping circles of decreasing radius according to a power law; the resulting set has fractal properties.

Contributed by: Enrique Zeleny (July 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The area of each circle decreases as , where is an integer and is an exponent between 1.1 and 1.5, which ensures convergence and interesting pictures. In fact, summing all areas gives the Riemann zeta function, with a starting area for the first circle satisfying the relation

.

For a high number of steps and values of near 1.5, the number of iterations required grows; in that case the number of iterations is limited to one million.

For a variety of designs, extensions to 3D, and estimates of fractal dimensions, visit Paul Bourke's web page.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send