Scal­ing Theory

23. September 2011

Within the past 40 years many arti­cles were pub­lished which show that log­a­rith­mic scal­ing invari­ance (“Scal­ing”) is a wide dis­trib­uted nat­ural phenomenon.

In 1967 /​ 68 Feyn­man and Bjorken dis­cov­ered the scal­ing phe­nom­e­non in high energy physics, con­crete in hadron col­li­sions. Simon E. Shnoll found scal­ing in the dis­tri­b­u­tions of macro­scopic fluc­tu­a­tions of nuclear decay rates. Since 1967 his team dis­cov­ers frac­tal scal­ing in the fluc­tu­a­tion dis­tri­b­u­tions of dif­fer­ent phys­i­cal and chem­i­cal processes, as well as in the dis­tri­b­u­tions of macro­scopic fluc­tu­a­tions of dif­fer­ent noise processes.

Within the fifties Beno Guten­berg and Charles Richter have shown, that exists a log­a­rith­mic invari­ant (scal­ing) rela­tion­ship between the energy (mag­ni­tude) and the total num­ber of earth­quakes in any given region and time period. In 1981, Leonid L. Chislenko pub­lished his exten­sive work on log­a­rith­mic invari­ance of the dis­tri­b­u­tion of bio­log­i­cal species, depen­dent on body size and weight of the organ­isms. By intro­duc­ing a log­a­rith­mic scale for bio­log­i­cally sig­nif­i­cant para­me­ters, such as mean body weight and size, Chislenko was able to prove that sec­tions of increased specie rep­re­sen­ta­tion repeat them­selves in equal log­a­rith­mic inter­vals. Knut Schmidt-​​Nielsen (1984) was able to prove scal­ing in bio­log­i­cal meta­bolic processes. Alexey Zhir­mun­sky and Vik­tor Kuzmin (1982) dis­cov­ered process-​​independent scal­ing in the devel­op­ment stages of embryo-​​, mor­pho– and onto­ge­n­e­sis and in geo­log­i­cal history.

Scal­ing is a fun­da­men­tal prop­erty of frac­tal struc­tures and processes. The Scal­ing The­ory explains the cause of the global scal­ing phenomenon.

See more Infor­ma­tion about the Scal­ing The­ory in Pub­li­ca­tions.

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