Biological systems are capable of dynamic self-organization, which involves the spontaneous emergence of spatio-temporal order and the formation of various patterns. Cells play a key role in organizing ontogenesis, with embryonic cells exhibiting coordinated behavior and generating ordered morphological patterns. Physical and topological patterns are essential for biological systems, as they restrict and direct morphogenesis. Biological self-organization is directed by natural selection, favoring sustainable, flexible, and modular systems. Self-organization is a fundamental property of complex systems, including biological ones, and is characterized by feedback, stability, flexibility, modularity, and hierarchy. Examples include gene regulatory systems, morphogenetic interaction networks, and connectivity graphs. Self-organization is inevitable in complex biological systems, such as those involving proteins with autocatalytic properties. Living systems are open, far-from-equilibrium systems that maintain themselves through continuous exchanges of matter, energy, and information. Biological self-organization is directed by natural selection and is characterized by nonlinear interactions, feedback, and hierarchy. Catastrophe theory, developed by Thom, shows that biological concepts can be expressed in terms of vector fields, attractors, and bifurcations. Strange attractors are intrinsic to nonlinear dynamical systems, including biological ones. Principles such as "omnis cellula e cellula" and "omnis membrana e membrane" have been established in biology. Eukaryotic cells contain self-reproducing organelles, such as mitochondria and chloroplasts, and centrosomes that regulate microtubule organization. Germinal granules are key organelles in germ line cells, controlling translation and transcription. Nonlinear interactions of elements can lead to complex behavior in biological systems, with the formation of ordered patterns based on chaotic dynamics. Excitable media, such as chemical reactions and biological systems, can exhibit spatio-temporal self-organization. Heterogeneous spatial patterns are common in living organisms, ranging from prokaryotic to multicellular. Bacterial colonies and eukaryotic unicellular organisms can self-organize into complex patterns. Aggregation of Dictyostelium amoebas is a classical example of biological self-organization. Synchronized collective behavior in animals, such as social insect colonies, shoals of fish, and flocks of birds, is considered an example of self-organization. Animal populations function as a whole, generating ordered patterns through nonlinear interactions. Social insects exhibit a simple, highly adaptive mechanism of collective intelligence with self-amplifying positive feedback.Biological systems are capable of dynamic self-organization, which involves the spontaneous emergence of spatio-temporal order and the formation of various patterns. Cells play a key role in organizing ontogenesis, with embryonic cells exhibiting coordinated behavior and generating ordered morphological patterns. Physical and topological patterns are essential for biological systems, as they restrict and direct morphogenesis. Biological self-organization is directed by natural selection, favoring sustainable, flexible, and modular systems. Self-organization is a fundamental property of complex systems, including biological ones, and is characterized by feedback, stability, flexibility, modularity, and hierarchy. Examples include gene regulatory systems, morphogenetic interaction networks, and connectivity graphs. Self-organization is inevitable in complex biological systems, such as those involving proteins with autocatalytic properties. Living systems are open, far-from-equilibrium systems that maintain themselves through continuous exchanges of matter, energy, and information. Biological self-organization is directed by natural selection and is characterized by nonlinear interactions, feedback, and hierarchy. Catastrophe theory, developed by Thom, shows that biological concepts can be expressed in terms of vector fields, attractors, and bifurcations. Strange attractors are intrinsic to nonlinear dynamical systems, including biological ones. Principles such as "omnis cellula e cellula" and "omnis membrana e membrane" have been established in biology. Eukaryotic cells contain self-reproducing organelles, such as mitochondria and chloroplasts, and centrosomes that regulate microtubule organization. Germinal granules are key organelles in germ line cells, controlling translation and transcription. Nonlinear interactions of elements can lead to complex behavior in biological systems, with the formation of ordered patterns based on chaotic dynamics. Excitable media, such as chemical reactions and biological systems, can exhibit spatio-temporal self-organization. Heterogeneous spatial patterns are common in living organisms, ranging from prokaryotic to multicellular. Bacterial colonies and eukaryotic unicellular organisms can self-organize into complex patterns. Aggregation of Dictyostelium amoebas is a classical example of biological self-organization. Synchronized collective behavior in animals, such as social insect colonies, shoals of fish, and flocks of birds, is considered an example of self-organization. Animal populations function as a whole, generating ordered patterns through nonlinear interactions. Social insects exhibit a simple, highly adaptive mechanism of collective intelligence with self-amplifying positive feedback.