Glossary

Is a set of states that a dynamical system is pulled toward over time and stays in once it arrives. No matter where the system starts (within a certain region called its basin of attraction), it ends up at the attractor and remains there or cycles inside it.

Common types include:

• Fixed-point attractor: The system settles into one unchanging stable state.
• Periodic (cycle) attractor: The system enters a repeating loop of states.
• Strange attractor: A complex, often chaotic pattern sensitive to starting conditions.

In Boolean networks (used to model gene regulation), attractors are especially important. A fixed-point attractor is a stable on/off pattern of genes, while a cyclic attractor is a repeating sequence of patterns. Biologists often interpret these as different cell types or stable phenotypes.In short, an attractor is the long-term stable pattern or “destination” a system settles into.

Are simple mathematical models made of nodes that can only be “on” (1) or “off” (0). Each node’s next state is decided by a logical rule (AND, OR, NOT, or combinations of these) based on the current states of the nodes connected to it. The entire network updates step by step in discrete time, either all at once (synchronous) or one node at a time (asynchronous). Over time the system settles into stable patterns called attractors—either a fixed state or a repeating cycle of states. First proposed by Stuart Kauffman in 1969 as models of gene regulatory networks, Boolean networks remain widely used in systems biology. They require little quantitative data yet still reveal how complex networks behave, stay robust against noise or mutations, and generate different cell types or phenotypes from the same set of genes.

Means the quality of being logical, consistent, and unified—parts that fit together clearly without contradictions or gaps. It describes something that makes sense as a whole: a coherent argument, plan, story, or explanation where ideas connect smoothly and support one another.

Is the spontaneous organization of colloidal particles—typically nanometer- to micrometer-sized particles suspended in a liquid—into ordered, larger-scale structures without external direction or intervention.

This process is widely used in materials science to create functional materials with tailored optical, mechanical, or electronic properties. Examples include photonic crystals (inspired by natural opals or butterfly wings), sensors, coatings, drug-delivery systems, and smart stimuli-responsive materials.

In essence, it is a powerful and scalable method for building complex nanostructures from simple colloidal building blocks by allowing physical and chemical forces to organize them.

Scientifically, describes systems of many interacting parts whose collective behavior produces emergent properties irreducible to the individual components. These systems exhibit nonlinearity, feedback, self-organization, and adaptation, yielding outcomes greater than the sum of their parts—such as in ecosystems, brains, or economies.It differs from mere complicatedness by featuring organized structure amid disorder. In information theory, Kolmogorov complexity measures the shortest program needed to generate an object. In computer science, computational complexity quantifies resources required to solve problems. Overall, complexity science studies these interdependent, adaptive phenomena across disciplines.

The total number of neighbour atoms, ions, or ligand donor atoms directly bonded to a central atom in a molecule, complex, or crystal.

A metaphysical view that all events within the universe can occur only in one possible way.

A pair or a group of two people, things, or units connected by a specific relationship. Derived from the Greek word dyas (meaning "two"), the term has specific technical definitions across sociology, biology, chemistry, and mathematics

A phenomenon in which complex systems and novel properties arise from the interactions of simpler components. The resulting whole displays behaviors or characteristics that the individual parts do not possess on their own and that cannot be fully predicted by examining those parts in isolation. Simple local rules or interactions at a lower level generate organized patterns at a higher level. Classic examples include flocks of birds forming coordinated shapes from each bird following basic rules of alignment and avoidance; ant colonies building elaborate nests and solving problems without any single ant directing the process; and the wetness or fluidity of water emerging from countless H₂O molecules. In biology, consciousness is frequently described as an emergent property of neural networks. In physics and chemistry, temperature, pressure, and phase transitions likewise arise collectively. Emergence underscores how complexity and order can self-organize without central control, making it a foundational concept in complexity science, systems theory, and the philosophy of science.

Face-Centered Cubic (FCC), also known as cubic close-packed (CCP), is one of the two densest possible arrangements of equal-sized spheres (the other being hexagonal close-packed, or HCP).

In this structure, identical spheres (such as atoms) stack in a highly efficient cubic pattern that fills 74% of the available space—the theoretical maximum packing density for spheres of the same size.

In short, FCC is a densely packed cubic arrangement that provides metals with excellent ductility and is commonly found in materials science and solid-state chemistry.

Global Workspace Theory (GWT), proposed by psychologist Bernard Baars in the 1980s, is a cognitive model of consciousness. It posits that the mind operates like a theatre: specialized, unconscious processors (the “audience”) handle perception, memory, and action in parallel, while a limited-capacity “global workspace” (the stage) selectively broadcasts information under the spotlight of attention.

Once information enters this workspace—via attentional selection—it becomes globally available to multiple brain systems, enabling flexible access, reportability, integration, and voluntary control. This broadcast accounts for the serial, unified nature of conscious experience amid massively parallel unconscious processing.

GWT emphasizes functional architecture over specific neural implementation, though later extensions (e.g., the Global Neuronal Workspace model) link it to widespread cortical ignition involving prefrontal and parietal networks. The theory remains influential in explaining access consciousness, the hard problem’s functional aspects, and phenomena such as inattentional blindness and the limits of working memory.

A pre-Socratic Greek philosopher from Ionia. Known as “the Obscure” for his cryptic style, only fragments of his work survive. He taught that reality is constant flux (panta rhei—everything flows), famously saying one cannot step into the same river twice. Fire represented the primary process of transformation. Beneath change lies the logos, an eternal rational order uniting all things. He stressed the unity of opposites: strife and harmony create dynamic balance, so conflicts form a coherent whole.His emphasis on process over static being, order emerging from continuous change and relational tension, and a unifying principle arising immanently continues to influence modern frameworks of relational emergence and geometric self-organization.

A German theoretical physicist and professor emeritus at the University of Stuttgart. He is best known as one of the founders of quantum-mechanical laser theory and the originator of synergetics, the interdisciplinary science of self-organization.In the 1960s, working independently of Willis Lamb, Haken developed a comprehensive quantum theory of the laser, interpreting the laser threshold as a nonequilibrium phase transition. This insight led him, in the late 1960s and 1970s, to create synergetics: a framework explaining how large numbers of interacting subsystems spontaneously form macroscopic order through “order parameters” and the “slaving principle.”His ideas influenced physics, chemistry, biology, cognitive science, and beyond. Haken authored more than 20 books and over 500 papers, founded the Springer Series in Synergetics, and received major honors including the Max Planck Medal, Pour le Mérite, and the Honda Prize. He died on 14 August 2024 at the age of 97.

Also called hexagonal close packing, is one of the two densest possible ways to arrange equal-sized spheres (atoms) in three dimensions. The other is face-centered cubic (FCC), also known as cubic close packing (CCP). Both achieve a packing efficiency of about 74%.

Because each atom has 12 neighbors, HCP (like FCC) is highly stable and dense. However, the hexagonal symmetry limits the number of independent slip systems compared with cubic metals. This often makes pure HCP metals less ductile at room temperature and more anisotropic (properties depend strongly on direction). Alloying and processing are commonly used to improve formability (e.g., in titanium and magnesium alloys used in aerospace and lightweight structures).In short, HCP is a fundamental crystal structure in materials science that describes how atoms pack most efficiently in a hexagonal pattern with alternating layers.

A philosophical and scientific view that systems must be understood as integrated wholes rather than mere collections of isolated parts. The whole possesses emergent properties that cannot be fully reduced to, or predicted from, its components alone—summarized in the phrase “the whole is greater than the sum of its parts.”Coined by Jan Smuts in Holism and Evolution (1926), the idea applies across domains. In biology and ecology it stresses the interconnectedness of organisms and environments. In psychology (notably Gestalt approaches) it treats the person as a unified mind-body system shaped by context. In medicine it advocates treating physical, psychological, and social dimensions together. In philosophy of science it opposes pure reductionism, arguing that higher-level patterns and relations are real and causally significant.Holism emphasizes relationships, context, and emergence: understanding any element requires seeing its place within the larger dynamic system.

In Ffellonics , a Level is one step in this fixed 12-stage hierarchy of relational emergence that structures the whole framework. It is generated by identical spheres following one local rule: symmetric nearest-neighbour attachment that maximises contacts while minimising free energy.

Each successive Level marks a discrete gain in symmetry, stability and relational depth.

One local rule (in Ffellonics) is the single, strictly local decision principle that governs every attachment: Identical spheres attach to their nearest neighbours only in the position that simultaneously

maximises the number of contacts,
preserves the highest possible symmetry of the existing cluster, and
produces the greatest reduction (or least increase) in Gibbs free energy.

No global plan, long-range force, or external blueprint is required. Every new sphere simply obeys this same local criterion, and the entire 12-Level hierarchy emerges as the cumulative, irreversible result.

The internal, individual, and subjective parts of a conscious experience, such as the redness of a rose, the sharp sting of pain, or the sweet taste of wine. The word comes from a Latin term meaning "of what sort".

A view that complex systems or phenomena can be fully understood and explained by breaking them down into their simplest, most fundamental parts and analyzing those parts in isolation. Higher-level properties are treated as nothing more than the sum of lower-level components and their interactions.Ffellonics stands in clear contrast to strict reductionism. While it begins with identical simple units (spheres), it insists that true reality and ordered structure arise only through relations. A single local rule—symmetric nearest-neighbor attachment that maximizes contacts while minimizing free energy—generates a 12-level hierarchy of progressive coordination, culminating in the stable 12-fold lattice. The higher levels and the ground-state harmony cannot be reduced to the properties of isolated spheres; they emerge from the cumulative relational process itself. Ffellonics therefore treats emergence and relational becoming as primary, rejecting the idea that the whole is merely the sum of disconnected parts.

A standardized, abstract conceptual framework. It maps out the core parts, concepts, and relationships of a system or process. Scientists and engineers use it as a common baseline to compare data, build specific simulations, and communicate ideas clearly without getting stuck on minor details.

A Hellenistic philosophy founded in Athens around 300 BC by Zeno of Citium. Named after the Stoa Poikile (“Painted Porch”) where he taught, it divides into logic, physics, and ethics.

Physics views the cosmos as ordered by divine reason (logos). Ethics is central: virtue—living in accordance with nature and reason—is the only true good and path to eudaimonia (flourishing). Externals such as wealth, health, or pain are “indifferent.” A wise person achieves apatheia (freedom from destructive passions) by focusing solely on what is within their control: judgments and actions. Stoics also stressed cosmopolitanism and rational acceptance of fate.

No early Stoic writings survive intact. The school influenced Romans like Seneca, Epictetus, and Marcus Aurelius, and its emphasis on resilience and self-mastery remains popular today.

Holds that certain higher-level properties or behaviours of a complex system cannot be deduced, predicted, or explained even in principle from complete knowledge of its lower-level components and their interactions. These properties are regarded as ontologically novel—genuine new features of reality rather than products of computational limits or incomplete information.

Unlike weak emergence, strong emergence asserts fundamental irreducibility. The higher-level phenomena may also involve downward causation, whereby the emergent properties influence or constrain the behaviour of the micro-level parts in ways not fully determined by the lower-level rules alone.

The concept is most frequently invoked in the philosophy of mind, where some theorists claim consciousness, subjective experience, or qualia strongly emerge from neural processes and resist reduction to purely physical descriptions. It remains controversial: many scientists and philosophers prefer weak emergence or strict reductionism, arguing that strong emergence risks violating the causal closure of the physical world or introducing unexplained dualism.

Weak emergence describes higher-level properties or patterns that arise from the interactions of a system’s simpler components and can, in principle, be fully derived, predicted, or simulated from complete knowledge of the lower-level rules, parts, and initial conditions—even when the calculation is extremely difficult or computationally intensive in practice.

These emergent features remain entirely determined by the micro-level dynamics. There is no fundamental ontological irreducibility or extra ingredient beyond the parts and their interactions. The novelty is epistemic, arising from our limited ability to track or compute the vast web of interactions.

Classic examples include bird flocks and fish schools generated by simple local alignment and avoidance rules, complex long-lived structures in Conway’s Game of Life, thermodynamic quantities such as temperature and pressure obtained via statistical mechanics, and traffic jams produced by individual driver decisions. Weak emergence is the form accepted by most scientists in complexity theory, physics, and systems science. It contrasts with strong emergence, which claims true, in-principle irreducibility of certain higher-level properties.

Werner Karl Heisenberg (1901–1976) was a German theoretical physicist who co-founded quantum mechanics. Born in Würzburg, he introduced matrix mechanics in 1925 and the uncertainty principle in 1927, earning the 1932 Nobel Prize in Physics.
His matrix formulation treats observables as non-commuting operators, while the uncertainty principle demonstrates that position and momentum cannot be simultaneously precise; measurement itself shapes what can be known. These ideas show that quantum properties are not fixed, intrinsic attributes of isolated particles but arise through mutual relations and observational contexts.
In this way Heisenberg’s work resonates with relational emergence: physical reality at the quantum scale is constituted by interdependent relations rather than pre-existing independent entities. Properties and states emerge from the dynamic web of interactions. He later advanced nuclear theory and directed the Max Planck Institute for Physics until his death in Munich.

He was a Hellenistic philosopher from Citium, Cyprus, and founder of Stoicism. Born to a merchant family, he came to Athens after a shipwreck (or trading voyage) and was inspired by Socrates via Xenophon’s Memorabilia. He studied under the Cynic Crates of Thebes and others, then taught from about 300 BC in the Stoa Poikile (“Painted Porch”), giving Stoicism its name.

His philosophy united logic, physics, and ethics. The highest good is virtue: living in accordance with nature and reason (logos). Externals like wealth or pain are indifferent. None of his works survive intact. He lived frugally, was honored by Athens, and is said to have died by suicide after a minor accident. He is distinct from the earlier Zeno of Elea.