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Fractal dimension of natural objects from nano-to-macro scale: an intrinsic property of material

Impact of road-space-rationing method on regional air quality

Source attributed premature mortality from ambient PM2.5 exposure

Aerosol acidity remains high despite declining sulfate concentration

Aerosol burden expected to increase in a warmer world

Challenges in quantifying aerosol-induced changes in cloud properties

Recent Indo-Pacific SST trends suppress rainfall in mid-latitude East Asia

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IASTA e-Bulltein |  Vol. 4 No.1 Home
To summarize, this article provides a brief introduction to the concept of fractals, and simple techniques to estimate the fractal dimension of crumpled paper balls and aerosols.

Fig. 3: The crumpled pieces of paper depicted in Fig. 2



Fig. 4: Plot of ln (M) vs. ln (d) for the crumpled balls

Suggested readings:

  • X Ma, M R Zachariah, and C D Zangmeister, Crumpled nanopaper from graphene oxide, Nano Lett., 12, pp.486-489, 2012.

  • J Luo, H D Jang, and J Huang, Effect of sheet morphology on the scalability of graphenebased ultra-capacitors, ACS Nano, 7(2), pp.1464–1471, 2013

  • M A F Gomes, Fractal geometry in crumpled paper balls, American Journal of Physics,55, pp.649, 1987.



  • M Amaku, L B Horodynski-Matsushigue, and P R Pascholati, The fractal dimension of breads, Phys. Teach., 37, pp.480, 1999.

  • B K Sapra, Y S Mayya, Arshad Khan, Faby Sunny, Sunil Ganju, and H S Kushwaha, Aerosol studies in a nuclear aerosol test facility under different turbulence conditions, Nuclear Technology, 163, pp.228-244, 2008.


Further readings:



Dr. S Anand
Health, Safety, and Environment Group, BARC, Trombay;

E-Mail: sanand@barc.gov.in

Dr. B K Sapra
Health, Safety, and Environment Group, BARC, Trombay;

E-Mail: bsapra@barc.gov.in

Dr. Y S Mayya
Department of Chemical Engineering, IIT Bombay, Mumbai

E-Mail: ysmayya@iitb.ac.in

© 2013 Indian Aerosol Science and Technology Association