Some Results on Multifractal Spectral Analysis


  • Roberto N. Padua
  • Efren O. Barabat University of San Jose-Recoletos
  • Mark S. Borres University of San Jose-Recoletos
  • Randy K. Salazar University of San Jose-Recoletos



multifractal, monofractal, λ(s)- spectrum, Legendre spectrum


A multifractal spectrum, based on an earlier paper and different from the Legendre multifractal spectrum (Padua et al. 2013) was examined in this paper. The examination yielded interesting results which enhanced the utility of the developed λ(s)-multifractal spectrum in analyzing real data. One of the results show that a mixture of several monofractal observations can be represented as a single monofractal distribution but whose spectrum is different from the spectrum of the original data. Thus, high fractal dimensional distributions can be infinitely decomposed into component monofractal dimensions. Further, we also show that given a multifractal set of observations, observations that fall on smaller scales obey a normal distribution. The study ends by providing possible avenues for future research particularly in the area of analytic number theory in relation to the Riemann hypothesis about the distribution of primes.

Author Biographies

Roberto N. Padua

Dr. Roberto Natividad Padua, scientist, received his PhD in Mathematical Statistics from Clemson University, South Carolina, USA under the Fullbright-Hays scholarship grant. He is an accomplished author, a multi-awarded researcher and an internationally acclaimed lecturer. Dr. Padua is a former Commissioner of CHED and currently a consultant to several state and private universities. He is also conducting lectures on research and Fractal Statistics. Dr. Padua is a Summa Cum Laude, BS in Mathematics Teaching graduate from the Philippine Normal College under the National Science Development Board (NSDB) program. He obtained his MS in Mathematics Education Degree from the Centro Escolar University as a Presidential Scholar.

Efren O. Barabat, University of San Jose-Recoletos

is an Electronics Engineer, graduated from the University of San Jose-Recoletos in 2010, Cum Laude honors. He ranked as top 9 examinee in the April 2011 ECE Licensure Examination. He worked as Field Engineer in SMART Communications, Inc. from 2011 to 2012. Currently, a full-time faculty member of the Electronics Engineering Department of USJ-R College of Engineering, handling Mathematics and Major Subjects of ECE.

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges.

Randy K. Salazar, University of San Jose-Recoletos

is a Mechanical Engineer, Assistant Professor of the University of San Jose Recoletos teaching Mechanical Engineering. Holder of a Masters in Science in Management Engineering from the University of San Jose Recoletos and finishing his Masters degree in Mechanical Engineering – Dynamic Design Systems at the University of San Carlos.


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How to Cite

Padua, R. N., Barabat, E. O., Borres, M. S., & Salazar, R. K. (2013). Some Results on Multifractal Spectral Analysis. Recoletos Multidisciplinary Research Journal, 1(2).




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