The Hausdorff dimension of some snowflake-like recursive constructions
UNSPECIFIED. (2002) The Hausdorff dimension of some snowflake-like recursive constructions. Nature, 10 (2). pp. 199-208. ISSN 0218-348XFull text not available from this repository.
Fractal subsets of R-n with a highly regular structure are often constructed as a limit of a recursive procedure based on contractive maps.
The Hausdorff dimension of recursively constructed fractals is relatively easy to find when the contractive maps associated with each recursive step satisfy the Open Set Condition (OSC). We present a class of random recursive constructions which resemble snowflake structures and which break the OSC. We calculate the associated Hausdorff dimension and conjecture that an a.s. deterministic exact Hausdorff function does not exist.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
|Journal or Publication Title:||Nature|
|Publisher:||WORLD SCIENTIFIC PUBL CO PTE LTD|
|Official Date:||June 2002|
|Number of Pages:||10|
|Page Range:||pp. 199-208|
Actions (login required)