Fractal Self-similarity, Scale Invariance and Stationary waves Codes Architecture Human Chromosomes DNA sequences

  • Jean-claude PEREZ


After demonstrating a method of numerical unification of DNA information at the level of each human chromosome, we have demonstrated the presence of periods and numerical "resonances" characterizing the DNA sequence of each human chromosome. We then analyze the fractal nature of these periods and numerical resonances by using a sample of reference human chromosomes in Sapiens and Neanderthal. In particular, we will demonstrate these properties of FRACTAL INVARIANCE by 3 types of results:

First proof: invariance of the periodic properties of chromosome 21 despite a random mixing of T C A G base-pairs.

Second proof: phenomena reminiscent of « discrete numerical waveforms » properties: resonances, dissonances, fractal periods, phase shifts, phase opposites. We will illustrate these properties by studying chromosomes 13 and 7 of Neanderthal and Sapiens HG38.

Third proof: invariance of the periodic properties of Sapiens HG38 chromosome 4 despite a regular sampling of the nucleotides (1 by 10 sampling then 1 by 100 sampling).

In this paper, we demonstrate the evidence of a robust INVARIANT at the global level of whole human chromosomes DNA sequences : « Law of chromosomal organization of the human genome », or " law of robustness of the chromosome " : Each chromosome (sapiens or neanderthal) is characterized by a spatial and fractal kind of "standing wave" (natural frequency) whose phase and period (in TCAG nucleotide number) appear to be determined not by the precise sequence but by the relative proportions of the TCAG base-pairs populations ".


[1] Lieberman-Aiden et al. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science, 2009; DOI: 10.1126/science.1181369 .
[2] Perez JC (1988) De nouvelles voies vers l'Intelligence Artificielle : pluri-disciplinarité, auto-organisation et réseaux neuronaux , Masson Publisher, Paris.
[3] Perez J.C, ''Fractal Chaos: a new neural network holographic model'', International Neural Networks Society (INNS) conference Boston USA in NEURAL NETWORKS international publication, 1988
[4] Perez j.c., La revolution des ordinateurs neuronaux, Hermes publisher Paris, 1990, ISBN-10: 2866012038,
[5] Perez JC (1990) Integers neural network systems (INNS) using resonance properties of a Fibonacci's chaotic `golden neuron'. IJCNN International Joint Conference,USA.
[6] Friedman R, Cross M (2013) The Golden Ratio & Fibonacci Sequence: Golden Keys to Your Genius, Health, Wealth & Excellence. 1st (Edn), Hoshin Media, USA.
[7] Pellionisz AJ, Graham R, Pellionisz PA , Perez JC (2012) Recursive Genome Function of the Cerebellum: Geometric Unification of Neuroscience and Genomics. In: Manto M, DL, et al. (Eds) Handbook of the Cerebellum and Cerebellar Disorders. 1st (Edn), Springer, USA.
[8] Rapoport DL (2015) Möbius strip and Klein Bottle Genomic Topologies, Self reference, Harmonics and Evolution, Life. Klein Bottle Logophysics, Self Reference, Heterarchies, Genomic Topologies, Harmonics and Evolution. Part III.
[9] Vaezi A, Barkeshli M (2014) "Fibonacci Anyons From Abelian Bilayer Quantum Hall States." Physical Review Letters 113. DOI: 10.1103/PhysRevLett.113.236804
[10] Hengwu Li, Daming Zhu, Caiming Zhang, Huijian Han, Keith A Crandall (2014) Characteristics and Prediction of RNA structure. BioMed Research International 8.
[11] Perez JC (1991) Chaos DNA and neuro-computers: a golden link. Speculations in Science and Technology 14: 336-346.
[12] Marcer PJ (1992) Order and chaos in DNA – the Denis Guichard Prizewinner: Jean-Claude Perez. Kybernetes 21: 60-61.
[13] Perez JC (1997) L'adn Décrypté. (1stedn), Resurgence publisher Liege, Belgium.
[14] Perez JC (2009) Codex Biogenesis. Resurgence, Liege Belgium.
[15] Perez JC (2010) Codon Populations in Single-Stranded Whole Human Genome DNA Are Fractal and Fine-Tuned by the Golden Ratio 1.618. Interdisciplinary Sciences: Computational Life Sciences 2: 1-13.
[16] Perez JC (2011) Caminos Interdisciplinaios. Seminario CLAVE_INTER, Espacio Interdisciplinario, Universidad de la Republica Montevideo, Uruguay.
[17] Perez JC (2011) Decoding Non-Coding DNA Codes: Human Genome Meta-Chromosomes Architecture. BIT Life Sciences’ 3rd Annual World Vaccine Congress, Beijing, China.
[18] Perez JC (2013) The “3 Genomic Numbers” Discovery: How Our Genome Single-Stranded DNA Sequence Is “Self-Designed” as a Numerical Whole. Applied Mathematics 4: 37-53.
[19] Perez J (2015) Deciphering Hidden DNA Meta-Codes -The Great Unification & Master Code of Biology. J Glycomics Lipidomics 5:131. doi: 10.4172/2153-0637.1000131 ,
[20] Perez J.C. , « DUF1220 Homo sapiens fractal periods architectures breakthrough » , to be published 2017.
[21] Perez J.C., "Humans and Primates Chromosomes4 Fractal CODES: periodic stationnary waveforms charaterizing and differenciating Neanderthal and Sapiens whole chromosomes DNA sequences", to be published 2017.
[22] Perez J.C., "Global and long range fractal differences between sapiens and neanderthal genomes", to be published 2017.
[23] Perez J.C. , "The Human Genome Optimum : a numerical universal law controling all LOH (Loss of heterozygosity) chromosomal deletions involved in human cancers ", to be published 2017.
[24] Perez J.C, .« Sapiens mtDNA circular long-range numerical meta-structures are highly correlated with mtDNA diseases mutations »., to be published in 2017.
[25] Neanderthal genome (2014)
[26] Sapiens Build34 (2003) genome
[27] Sapiens HG38 (2013) genome
[28] Dokukin ME, Guz NV, Woodworth CD, Sokolov I (2015) Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer. New J Phys 17
[29] Petoukhov S (2011) Mathematics of Bioinformatics: Theory, Methods and Applications. 1st (Edn), John Wiley & Sons, USA.
[30] Montagnier L, Aïssa J, Ferris S, Montagnier JL, Lavallée C (2009) Electromagnetic Signals Are Produced by Aqueous Nanostructures Derived from Bacterial DNA Sequences. Interdiscip Sci Comput Life Sci 1: 81-90.
[31] Persaud, Dharam and O'Leary, James P., "Fibonacci Series, Golden Proportions, and the Human Biology" (2015). HWCOM Faculty Publications. Paper 27.
[32] Roman V Yampolskiy, On the origin of synthetic life: attribution of output to a particular algorithm, The Royal Swedish Academy of Sciences , Phys. Scr. 92 (2017), DOI : 10.1088/0031-8949/92/1/013002
[33] Syracuse conjecture,
[34] Buffa Pietro , I Geni Manipolati di Adamo – Libro Le origini umane attraverso l'ipotesi dell'intervento biogenetico,
[35] Marshall P (2011) Evolution 2.0. Benbella Books, USA.
[36] Perez JC (2017) The “Master Code of DNA”: Towards the Discovery of the SNPs Function (Single-Nucleotide Polymorphism). J Clin Epigenet. Vol. 3 No. 3:26
[37] Perez, J.C. (2017), The “Master Code of Biology”: Self-assembly of two identical Peptides beta A4 1-43 "Amyloid" in Alzheimer’s Diseases. Biomed J Sci & Tech Res 1(4)-2017.
[38] Perez, J.C. (2017), The «Master Code of Biology»: from Prions and Prions-like Invariants to the Self-assembly Thesis. Biomed J Sci & Tech Res 1(4)-2017.
[39] Perez J.C., (2017) "Humans and Primates Chromosomes4 Fractal CODES: periodic stationnary waveforms charaterizing and differenciating Neanderthal and Sapiens whole chromosomes DNA sequences" , (paper to be published, 2017).
[40] Perez, J.C., Decyphering “the MASTER CODE ®” Structure and Discovery of a Periodic Invariant Unifying 160 HIV1/HIV2/SIV Isolates Genomes. Biomed J Sci & Tech Res 1(2)-2017. BJSTR. MS.ID.000209.
[41] Perez J.C., (2017), Symmetry and Asymmetry in the MENDELEEV’s Periodic Table Predictive EQUATION(2017)SDRP Journal of Computational Chemistry & Molecular Modelling 2(1) 20and 20Asymmetry 20in20the 20MENDELEEV’s 20Periodic 20Table 20Predictive20EQUATION/224
[42] Perez JC (2017) Sapiens Mitochondrial DNA Genome Circular Long Range Numerical Meta Structures are Highly Correlated with Cancers and Genetic Diseases mtDNA Mutations. J Cancer Sci Ther 9:512-527. doi: 10.4172/1948-5956.1000469
[43] Perez J, DUF1220 Homo Sapiens and Neanderthal fractal periods architectures breakthrough(2017)SDRP Journal of Cellular and Molecular Physiology 1(1) 20and20Neanderthal20 20fractal 20 periods20architectures 20breakthrough/184?
How to Cite
PEREZ, Jean-claude. Fractal Self-similarity, Scale Invariance and Stationary waves Codes Architecture Human Chromosomes DNA sequences. Bioinformatics and Computational Biology Letters, [S.l.], v. 1, n. 1, p. 1-26, oct. 2017. Available at: <>. Date accessed: 17 dec. 2018.