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Using Blinking Fractals for Mathematical Modeling of Processes of Growth in Biological Systems

A New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-030-93642-6_1
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 3
A Numerical Approach to Basic Calculus
Layla Nasr
https://doi.org/10.1007/978-3-031-81247-7_32
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 338
A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic
P. Amodio, F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev
https://doi.org/10.1016/j.matcom.2016.03.007
Journal  Mathematics and Computers in Simulation Volume 141 (2017), p. 24
A mathematical investigation on the invariance problem of some hydraulic indices
Fabio Caldarola, Mario Maiolo
https://doi.org/10.1016/j.amc.2020.125726
Journal  Applied Mathematics and Computation Volume 409 (2021), p. 125726
A new approach to the Z-transform through infinite computation
Fabio Caldarola, Mario Maiolo, Viviana Solferino
https://doi.org/10.1016/j.cnsns.2019.105019
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 82 (2020), p. 105019
AIP Conference Proceedings
F. Mazzia, Ya. D. Sergeyev, F. Iavernaro, P. Amodio, M. S. Mukhametzhanov
https://doi.org/10.1063/1.4965397
Conference  Volume 1776 (2016), p. 090033
AIP Conference Proceedings
Yaroslav D. Sergeyev
https://doi.org/10.1063/1.5043649
Conference  Volume 1978 (2018), p. 020004
Addressing Ill-Conditioning in Global Optimization Using a Software Implementation of the Infinity Computer
Marat S. Mukhametzhanov, Dmitri E. Kvasov
https://doi.org/10.1007/978-3-030-93642-6_14
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 347
Adopting the Infinity Computing in Simulink for Scientific Computing
Alberto Falcone, Alfredo Garro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-030-93642-6_13
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 313
Computation of supertrack functions for Chua’s oscillator and for Chua’s circuit with memristor
Fabio Caldarola, Pietro Pantano, Eleonora Bilotta
https://doi.org/10.1016/j.cnsns.2020.105568
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 94 (2021), p. 105568
Computations with Grossone-Based Infinities
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-21819-9_6
Book  Lecture Notes in Computer Science (Unconventional Computation and Natural Computation) Volume 9252 (2015), p. 89
Examples of the Usage of Infinities and Infinitesimals in Numerical Computations
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-12745-3_15
Book  Communications in Computer and Information Science (Advances in Artificial Life and Evolutionary Computation) Volume 445 (2014), p. 190
Fibonacci words, hyperbolic tilings and grossone
Maurice Margenstern
https://doi.org/10.1016/j.cnsns.2014.07.032
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 3
Game Theory Presented to Italian High School Students in Connection with Infinity Computing
Corrado Mariano Marotta, Andrea Melicchio
https://doi.org/10.1007/978-3-031-81247-7_11
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 139
Grossone Infinity Computing
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-1-4939-6883-1_685
Book  (2018), p. 663
Grossone Infinity Computing
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-642-27737-5_685-1
Book  (2017), p. 1
Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite
Yaroslav D. Sergeyev
https://doi.org/10.1007/s10699-018-9566-y
Journal  Foundations of Science Volume 24, Issue 1 (2019), p. 153
Infinigons of the hyperbolic plane and grossone
Maurice Margenstern
https://doi.org/10.1016/j.amc.2016.01.019
Journal  Applied Mathematics and Computation Volume 278 (2016), p. 45
Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves
Luigi Antoniotti, Fabio Caldarola, Mario Maiolo
https://doi.org/10.1007/s00009-020-01531-5
Journal  Mediterranean Journal of Mathematics Volume 17, Issue 3 (2020)
Infinity computations in cellular automaton forest-fire model
D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa
https://doi.org/10.1016/j.cnsns.2014.06.031
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 20, Issue 3 (2015), p. 861
Introduction
Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
https://doi.org/10.1007/978-1-4614-8042-6_1
Book  SpringerBriefs in Optimization (Introduction to Global Optimization Exploiting Space-Filling Curves) (2013), p. 1
Legal Systems and Fractals, Towards Infinity Computing
Maria Rita Maiolo, Mària Ivano
https://doi.org/10.1007/978-3-031-81247-7_29
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 316
Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm
Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev
https://doi.org/10.1016/j.amc.2017.05.058
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 298
New Approaches to Basic Calculus: An Experimentation via Numerical Computation
Luigi Antoniotti, Fabio Caldarola, Gianfranco d’Atri, Marco Pellegrini
https://doi.org/10.1007/978-3-030-39081-5_29
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 329
Noise-induced kinetic transition in two-component environment
Dmitry I. Iudin, Fedor D. Iudin, Artem A. Syssoev, Vitaly Yu. Klimashov, Alexey A. Emelyanov
https://doi.org/10.1016/j.cam.2020.113268
Journal  Journal of Computational and Applied Mathematics Volume 388 (2021), p. 113268
Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications
Renato De Leone
https://doi.org/10.1016/j.amc.2017.03.029
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 290
Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications
Yaroslav D. Sergeyev
https://doi.org/10.1007/978-1-4614-7582-8_1
Book  Springer Proceedings in Mathematics & Statistics (Dynamics of Information Systems: Algorithmic Approaches) Volume 51 (2013), p. 1
Numerical infinitesimals in a variable metric method for convex nonsmooth optimization
Manlio Gaudioso, Giovanni Giallombardo, Marat Mukhametzhanov
https://doi.org/10.1016/j.amc.2017.07.057
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 312
On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales
Yaroslav D. Sergeyev, Dmitri E. Kvasov, Marat S. Mukhametzhanov
https://doi.org/10.1016/j.cnsns.2017.11.013
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 59 (2018), p. 319
On the topological convergence of multi-rule sequences of sets and fractal patterns
Fabio Caldarola, Mario Maiolo
https://doi.org/10.1007/s00500-020-05358-w
Journal  Soft Computing Volume 24, Issue 23 (2020), p. 17737
Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions
Fabio Caldarola, Domenico Cortese, Gianfranco d’Atri, Mario Maiolo
https://doi.org/10.1007/978-3-030-39081-5_31
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 358
Percolation Transition and Related Phenomena in Terms of Grossone Infinity Computations
Dmitry I. Iudin, Yaroslav D. Sergeyev
https://doi.org/10.1007/978-3-319-33924-5_11
Book  Emergence, Complexity and Computation (Advances in Unconventional Computing) Volume 22 (2017), p. 239
Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming
Renato De Leone, Giovanni Fasano, Yaroslav D. Sergeyev
https://doi.org/10.1007/s10589-017-9957-y
Journal  Computational Optimization and Applications Volume 71, Issue 1 (2018), p. 73
Representation of grossone-based arithmetic in simulink for scientific computing
Alberto Falcone, Alfredo Garro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev
https://doi.org/10.1007/s00500-020-05221-y
Journal  Soft Computing Volume 24, Issue 23 (2020), p. 17525
Reprint of Infinity computations in cellular automaton forest-fire model
D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa
https://doi.org/10.1016/j.cnsns.2014.10.019
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 190
Single-tape and multi-tape Turing machines through the lens of the Grossone methodology
Yaroslav D. Sergeyev, Alfredo Garro
https://doi.org/10.1007/s11227-013-0894-y
Journal  The Journal of Supercomputing Volume 65, Issue 2 (2013), p. 645
Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
Yaroslav D. Sergeyev
https://doi.org/10.1016/j.amc.2013.04.019
Journal  Applied Mathematics and Computation Volume 219, Issue 22 (2013), p. 10668
Solving the Lexicographic Multi-Objective Mixed-Integer Linear Programming Problem using branch-and-bound and grossone methodology
Marco Cococcioni, Alessandro Cudazzo, Massimo Pappalardo, Yaroslav D. Sergeyev
https://doi.org/10.1016/j.cnsns.2020.105177
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 84 (2020), p. 105177
The Cantor-Vitali Function and Infinity Computing
Luigi Antoniotti, Corrado Mariano Marotta, Andrea Melicchio, Maria Anastasia Papaleo
https://doi.org/10.1007/978-3-031-81247-7_18
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 232
The Grossone Methodology Perspective on Turing Machines
Yaroslav D. Sergeyev, Alfredo Garro
https://doi.org/10.1007/978-3-319-09039-9_7
Book  Emergence, Complexity and Computation (Automata, Universality, Computation) Volume 12 (2015), p. 139
The Grossone-Based Diagonal Bundle Method
Manlio Gaudioso, Giovanni Giallombardo, Marat S. Mukhametzhanov
https://doi.org/10.1007/978-3-030-93642-6_7
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 167
The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities
Yaroslav D. Sergeyev
https://doi.org/10.1007/s00283-014-9511-z
Journal  The Mathematical Intelligencer Volume 37, Issue 2 (2015), p. 4
The Role of grossone in Nonlinear Programming and Exact Penalty Methods
Renato De Leone
https://doi.org/10.1007/978-3-030-93642-6_3
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 77
The Sierpinski curve viewed by numerical computations with infinities and infinitesimals
Fabio Caldarola
https://doi.org/10.1016/j.amc.2017.06.024
Journal  Applied Mathematics and Computation Volume 318 (2018), p. 321
The Use of Infinities and Infinitesimals for Sparse Classification Problems
Renato De Leone, Nadaniela Egidi, Lorella Fatone
https://doi.org/10.1007/978-3-030-93642-6_6
Book  Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 151
The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area
Yaroslav D. Sergeyev
https://doi.org/10.1016/j.cnsns.2015.07.004
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 31, Issue 1-3 (2016), p. 21
The exact measures of the Sierpiński d-dimensional tetrahedron in connection with a Diophantine nonlinear system
Fabio Caldarola
https://doi.org/10.1016/j.cnsns.2018.02.026
Journal  Communications in Nonlinear Science and Numerical Simulation Volume 63 (2018), p. 228
Unimaginable Numbers and Infinity Computing at School: An Experimentation in Northern Italy
Luigi Antoniotti, Annabella Astorino, Fabio Caldarola
https://doi.org/10.1007/978-3-031-81247-7_17
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 223
Unimaginable Numbers: a Case Study as a Starting Point for an Educational Experimentation
Francesco Ingarozza, Gianfranco d’Atri, Rosanna Iembo
https://doi.org/10.1007/978-3-031-81247-7_9
Book  Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 113
Usage of infinitesimals in the Menger’s Sponge model of porosity
Maria C. Vita, Samuele De Bartolo, Carmine Fallico, Massimo Veltri
https://doi.org/10.1016/j.amc.2011.06.013
Journal  Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8187


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