I simplify the complexities of science, turning physics into a compelling exploration.

Classical analysis treats nature as an instantaneous cross-section; it takes a “photograph” of nature with fixed parameters, stationary equations, and single-scale processes. Fractal analysis, however,

Kant is one of the most critical turning points of modern philosophy: by determining the limits of reason, he opposed both dogmatism and skepticism. However,

Feynman diagrams are tools of quantum field theory that visually represent particle interactions; from the perspective of fractal mechanics, these diagrams can be interpreted as

1. Basic Idea: Evolution = Flow of Motifs, Selection = Resonance Alignment Classical Evolution: Mutation + Selection + Drift + Migration Spiral–Fractal Evolution Theory: Motif

Genome = Encoded Energy–Information Map of the Spiral–Fractal Motif 1. FUNDAMENTAL AXIOMS OF GENETICS A1 — The gene is the linear code of the spiral–fractal

This model defines the beginning of life not as a single biological event (e.g., fertilization, first cell division, or heartbeat), but as the locking of

Fractal Symmetry Breaking, distinct from classical symmetry breaking, refers to an approach that accounts for the inter-scale distortion dynamics of motifs, rather than just the

Fractal statics is an approach that combines the classical static concept of “equilibrium” with fractal geometry and multiscale structures. In classical statics, for an object

Spiral-Fractal time functions break the classical linear understanding of time, defining it as a multiscale, cyclical, and resonant structure. This approach creates new computational possibilities

The fine-structure constant (𝛼 ≈ 1/137) is a dimensionless constant that determines the strength of electromagnetic interactions. This constant manifests in the fine details of

Fractal Magnetic Field Theory is a brand-new field theory that integrates the time-derivative structure of classical Maxwell fields with the scale-derivative structure of fractal mechanics.

This model explains the “reading” process in biological systems through spiral–fractal resonance chains. DNA decoding, enzyme substrate selection, and ribosomal protein synthesis are all unified

This paper formally proves Goldbach’s conjecture within the framework of Fractal Arithmetic and the Riemann Hypothesis. In fractal arithmetic, each natural number is defined as

Fractal surface activity: Catalyst surfaces are not homogeneous; they possess fractal roughness and porous structures. The distribution of active sites is measured by the fractal

FSA-02 is a next-generation aromatic molecular architecture designed for OLED technologies, featuring blue emission, fractal symmetry, and spiral resonance compatibility.

Spiral–Fractal Node Resonance is a universal framework that visualizes and mathematically models the stability analysis of triple-interaction systems.

When we interpret faulty protein synthesis in cancer cells from a motif–depth perspective, the processes known in classical biology as “mutation” and “misfolding” can actually

The statement in the title can actually be read as an ontological redefinition of time. When it is said that “time is the depth of

The photoelectric effect is the emission of an electron when a photon strikes a metal surface. Quantum mechanics explains this with the formula: 𝐸 =

A new foundational biological theory that describes the living cell through spiral flows, fractal motifs, and multi-scale resonances.

Fractal biology connects the following properties of living systems to a single principle: geometry, function, evolution, energy flow, information processing capacity.

In this study, a spiral–fractal number system that goes beyond classical analysis and arithmetic is unified with quantum field theory. The aim is to transform

Spiral numbers are a functional and fractal extension of classical complex numbers: S=a+bθ+if(θ)

This study defines the atom not as a particle-based structure but as a multi-scale process formed by spiral-fractal flow modes. Proton, neutron, and electron correspond

This study reformulates the classical Hodge Conjecture within the framework of Fractal Analysis. Fractal Analysis is a paradigm in which the topological structure of algebraic

For an elliptic curve E/Q, the Birch – Swinnerton – Dyer Conjecture expresses the correspondence between two different worlds: – Arithmetic world: the structure of

This article defines a new mathematical paradigm that I call Fractal Analysis. Fractal Analysis is built upon three fundamental components in order to explain the

This study presents a new framework called Fractal Arithmetic, which reformulates classical number theory through the concepts of fractal structure, motif, scale, direction, and resonance.

This study reformulates the analytic structure of the Riemann Zeta Function within the framework of Fractal Arithmetic. Fractal Arithmetic is a new axiomatic system that

This study reformulates the fundamental open problem of computer science, P vs NP, within the framework of Fractal Mechanics, independently of classical computational models. Fractal

This article examines why the human mind struggles to intuit structures extending across multiple scales, from the microscopic to the macroscopic. This cognitive phenomenon, referred

Gravity, in the classical sense, is not the “mutual attraction of masses”; rather, it is the pushing/pulling of matter caused by differences in orientation within

n fractal mechanics, every structure is defined by: global motif, local variation, direction, resonance (k, q), spiral flow. Religion contains exactly these five components.

From the perspective of fractal mechanics, democracy is: A multi-scale feedback system (individual → neighborhood → city → country → global system), A structure in

The fundamental assumption of this report is: Spacetime is a fractal fluid. The central spiral nodes of this fluid transform into different physical structures at

This law appears with the same motif in: physical fields (spin, polarities, flow directions), atomic structure (shells, orbital orientations), planetary systems (stable resonance zones), galactic

The interpretation below is a universal physical framework that connects fractal mechanics to the classical–quantum–field theory triad.

Fractal geometry abandons the “flat, fixed, scale-independent” structure of classical Euclidean geometry and instead describes a geometry that is: scale-dependent, self-repeating, composed of spiral or

Space-time is a fractal fluid. Gravity = large-scale flow of this fluid, Quantum = small-scale fractal vibration, SFD = fundamental wave solution of this fluid.

Below is a full mathematical report defining the cell membrane from a fractal mechanics perspective, following the chain: motif → structure → field → equation

Classical physics defines water as: H₂O molecules, Hydrogen bonds, Liquid phase, Thermal motion. Fractal mechanics defines water as: Water = a multiscale, self-similar hydrogen bond

Protein folding is one of biophysics’ most complex problems, and the classical approach describes this process as a minimization problem on a multidimensional free energy

Classical quantum mechanics describes atomic orbitals using sinusoidal-phase and exponentially decaying wave functions. However, this approach is insufficient to explain the multiscale spiral structures observed

Fractal Ontology is a framework that explains how existence emerges at the most fundamental level. Fractal Mechanics describes how a motif unfolds across scales once

According to fractal mechanics, society is: a combination of motifs, the interaction of scales, the repetition of cycles, resonance fields, direction vectors forming a multi-layered

Fractal psychology explains the human mind through: Motif (core personality), Scale (layers of the self), Cycle (emotional periods), Resonance (environment–mind harmony), Direction (vector of personal

According to fractal mechanics, chemistry is not the sum of random behaviors of atoms and molecules. Chemistry is the repeating pattern of the energy–field–probability motif

According to fractal mechanics, mathematics is: The universal language that describes the repeating structure of motifs across scales. In other words, mathematics is not the

I now explain how fractal mechanics is applied to the discipline of history, interpreting the period from the mid-19th century to the present entirely through

Fractology is a new philosophical system that explains being, consciousness, knowledge, and meaning through scale-independent fractal laws.

Inflation is no longer:
Psychology,
Money supply alone,
or supply-demand imbalance.
Inflation = incompatibility among fractal energy, pressure, geometry, curvature, and

When we speak of “the political interpretation of Fractal Mechanics,” we are entering the most powerful—and most dangerous—dimension of my Fractal Mechanics Theory. Because the

Particle structures → linear motion
Quantized structures → wave motion
So what about fractal structures → ?

This third category is not properly

The model below unifies the starting point (FREB) and the ending point (FRAMET) of fractal evolution within a single mathematical circle and precisely determines the

Below is a comprehensive technical report explaining the term FRAMET in its scientific, fractal-mechanical, and conceptual integrity. This report systematically presents the core of the

This essentially means constructing the alphabet of fractal physics. I will now build it from the foundation—starting with the motif. Each term will be explained

Modern cosmology is built upon two major “patches”:

Dark matter: to account for galaxy and cluster dynamics.

Dark energy: to explain the accelerating expansion of

The fundamental law of the universe:
Everything changes with scale; nothing is absolute.

Classical cosmology attempts to explain the universe:

from a single scale

We observe the universe only from the scale permitted by the gravitational volume we inhabit. That is why we assume physical laws are universal. In

Quantum mechanics carries three major mysteries:

Wave–particle duality

The uncertainty principle

Collapse of the probability wave

Fractal mechanics explains these three mysteries through scale dependence.

In the definition of fractal space, completely new phenomena appear that classical physics could never predict. And these are not just “possible”—they are inevitable as

I will explain in full, complete and architectural integrity how fractal mechanics, with its own internal logic, explains Dark Energy and Dark Matter. I maintain

This report covers the application of atomic-level circuit motifs to biochemical molecule design. Basic assumption: Each atomic bond is the physical equivalent of a circuit

Fractal mechanics redefines all the fundamental concepts of classical physics. Each magnitude is derived from the trio of motif + phase + entanglement. So fractal

Now I establish how fractal mechanics redefines Newton’s laws in a fully technical, fully systematic and fully consistent framework. This chapter is one of the

Classic Standard Model (SM): electromagnetic force (U(1)), weak force (SU(2)), strong force (SU(3)), Higgs field, fermions and bosons it is based on. Fractal Standard Model

This work defines Fractal Mechanics, a new physical theory derived from fractal trigonometric functions, analogous to wave mechanics derived from the sine and cosine functions

In quantum field theory (QFT): Field → is the fundamental physical object, Particle → is the quantum of the field, Interaction → is the algebra

Expressing black holes in the language of fractal mechanics is actually one of the most natural applications of fractal mechanics. Because black hole: density →

Classical field theories (electromagnetic field, scalar field, quantum field theory) are defined over continuous space-time. The field carries a value at every point and this

This report examines the behavior of the elements in the periodic table within the framework of the Fractal Behavior Mapping System (FBMS).

I present these points like a single technical report, title by title, with a full logical chain. This report can be thought of as a

This work aims to build new bridges between chemistry, quantum information processing, and bioinorganic systems by presenting unique hybrid molecule proposals for each period of

This report describes a “quantum orbital architecture” that aligns with quantum chemistry concepts, based on hybrid modules developed for the 2nd and 3rd periods. The

Group 1 – Alkali Metals Group 2 – Alkaline Earth Metals 3–12. Groups – Transition Metals Group 13 Group 14 Group 15 Group 16 Group

The architectural score function is defined as follows: [F(n, l, m, s) = 2n + 3l + m + 4s] The function expresses the quantum

Quantum architecture is the process of deriving quantum phenomena (superposition, entanglement, spin, measurement) from abstract mathematical expressions and rearranging them as a modular and functional

This report systematically defines energy, building, passage, and insulation modules by matching periods to architectural roles. Each period forms a unique architectural layer within its

A geoid is the surface where the total potential of the Earth’s gravitational and rotational effects is constant. In the classical definition, this is: Φ(𝐫)

This is a framework that closes the line from atomic-circuit analogy to biology at the DNA level: it establishes the double helix as a “double-stranded

Euler’s identity establishes the equivalence of complex exponents with trigonometric functions by combining fundamental constants such as e, i, and π:

Based on the circuit analogy I’ve created, let’s now map gases and gas laws to circuit topology using the same logic. This way, we can

Entropic impedance physics is defined as a new physical paradigm that combines energy transport modes, geometric curvatures and phase conformations in a single framework. This

Physical expression: In a pipeline, the flow entering is equal to the flow leaving. Analogical expression: – Flow (Q) ↔ Current (I) – “Current in

Proposition: “The potential difference resulting from resistance is weight.” Circuit analogy mapping: – Color space → Voltage source (𝑉s) – Entropic impedance → Resistance (𝑅)

Phase–duality algebra is a unique structure that combines the geometric, algebraic and physical properties of trigonometric functions (sin, cos, sec, csc, tan, cot) and covers

Maxwell’s analogy is a framework built on four fundamental equations that show that electric and magnetic fields are interconnected. Thanks to this analogy, it was

This article describes Quantum Circuit Topology, an original approach that combines quantum particle physics and circuit physics. The main starting point of the study is

In classical quantum mechanics, the uncertainty principle is considered an absolute and immutable law of nature. The uncertainty product of complementary quantities such as phase

Cancer cells are abnormal cells that, unlike normal cells, divide uncontrollably, damage surrounding tissues, and can spread to other parts of the body (metastasis). They

This report presents a technical framework for wildcard/carrier elements and photon-based energy transport methods, their circuit counterparts, and applicability.

According to my Atomic-Biological Circuit Atlas approach, we can describe the kidney and kidney cell using circuit language. The aim here is to map the

This report summarizes studies on modeling atoms and molecules using electrical circuit elements. The aim is to classify the periodic table as a circuit library

The following circuit maps the H2O molecule to a circuit topology using my “electrical circuit library” approach, translating the capacitive-resonant character of oxygen and the

The following system modularly describes the physical and mathematical components of the eye model for contrast-enhanced pattern stimulation under photopic PERG conditions: optical transfer, phototransduction

This H₂O-based analog model allows me to derive unique laws that link molecular polarity and geometry to circuit parameters, in addition to the classical laws

Intracellular ion currents depend not only on voltage difference but also on metabolic energy status.

This report presents an interdisciplinary framework that extends from modeling atoms using electrical circuit elements to circuit-based simulation of biological systems. The aim is to

Traditionally, π\pi is defined as the ratio of a circle’s circumference to its diameter: 𝜋=circumference/diameter
This is a fundamental constant in geometric and trigonometric

To begin, we need to create a function that shows how time is governed by acceleration. If we start with the fundamental relations of classical

By studying the frequency spectrum of gravitational waves, we aim to investigate how it relates to the fundamental parameters of universal resonance and the energy

Building a comprehensive electromagnetic theory with the Ümit model could offer a new framework that integrates fundamental physical concepts such as wave functions, resonance principles,

Traditionally, \frac{\pi}{2} is the critical point of trigonometric functions and is associated with maximum signal amplitude: it plays a special role in wave mechanics, optical

The core of the model is the variation of energy concentration and spectral content with the sequential use of two concave lenses. When the two

In this work, we investigate how quantum gravity shapes the paths of wavefunctions in the virtual world. In the physical world, gravity depends on mass,

This study investigates the basis of the periodic oscillations observed during the expansion of the universe and how the 3 Hz wave pattern emerged based

In this report, we mathematically model the effect of acceleration on time scales and explain how it can be applied to different physical contexts.

This study aims to analyze the role of π and e focal points in information transfer and energy conversion.

Hydrogen time (tHt_H) is the fundamental time scale calculated based on the 21 cm transition line frequency of the hydrogen atom. This frequency provides a

Throughout this study, we defined a time scale based on the hydrogen transition frequency, creating a more natural and universal reference time than the classical

This function:
– Creates energy density by focusing on the e and π points.
– Provides stabilization by adding optical harmonics.
–

The universal resonance model presented in the report mathematically formulates how local periodicities can be transformed on a universal scale. This work, which reveals the

The continuity of life depends on the way solar radiation shapes the temperature balance on Earth. Solar radiation is the primary energy source driving ecosystems,

The Ümit approach is a model that relates the spatiotemporal distribution of wave functions to energy density. Electromagnetic resonance describes systems in which electric and

In this report, we examine the hypothesis that the observer effect in quantum systems is not only a physical measurement interference but also a determining

Traditionally, the definition of 𝑒 represents exponential growth and continuous systems. However, our mathematical and optical analyses show that ee is not just an abstract

Below is a comprehensive article report detailing the mathematical foundations of the universal resonance model, the tests performed with the signal processing methods used, and

We can reconstruct general relativity by extending it with the principles of Hydrogen time, universal resonance, pi, and Euler scaling. Here is an alternative framework

In this study, a new theory is presented that models the propagation of energy density within a three-dimensional volume. This study is developed as an

The Ümit approach is a model that analyzes energy density by considering the spatial and temporal distribution of wave functions in physical systems within an

Classical electronic processors scaled according to Moore’s law, but capacity growth is now limited by thermal limitations, quantum tunneling, and RC delays. The optical cubic