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This fractal cosmology is distinct from other types of fractal cosmologies. The fractal cosmos described herein is distinct from the application of fractals to astronomy to describe the fractal distribution of galaxies within the visible universe. Also, the present fractal cosmology is distinct from the multiple universes (multiverses) of “eternal inflation,” which are based on quantum field theory; and the “black hole within black hole” multiverses, which are based on general relativity. Rather, the fractal cosmos that is described herein is an integrated fractal structure that allows for the development of an orderly sequence of universes. This fractal cosmos gives birth to distinct fractal-like universes of different orders of magnitude. Our own universe can be assigned a specific rank within a hierarchical series of universes.


This unique fractal cosmology is based on a theory proposed by Harry Walter Schmitz (1923-1979) many years before the word “fractal” was introduced into our vocabulary by Mandelbrot in the 1970s. If you are interested in learning about this fractal cosmology then please begin your adventure with the Fractal Cosmos Grand Tour. Also, the papers below can be downloaded and studied to obtain a profound understanding of the fractal cosmos, including fractal universes, fractal particles, fractal particle mechanics, fractal particle interactions and a theory of gravity in a fractal universe.


Harry A. Schmitz

May 2008



Harry A. Schmitz, Ph.D.
Fractal Cosmos Research Institute
18 Pequot Ave
Port Washington, NY 11050

+1(516) 414-0698




Fractal Cosmos Grand Tour: Follow through the topics of the introductory tour in sequence until a basic understanding of the fractal cosmos emerges. These simple ideas add up to a truly amazing fractal cosmos.
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On the Role of the Fractal Cosmos in the Birth and Origin of Universes
By Harry A. Schmitz

A fractal model of the cosmos is presented in terms of distinct orders of universes, particles, substrates and strata. Each universe in the fractal cosmos is characterized by the radius of that universe divided by the effective radius of one of its stratum particles. It is shown that this size ratio increases rapidly for higher order universes and that a series of universes of descending order must terminate with the visible universe. The fractal cosmos is a single integral whole that gives birth to many generations of universes.

REFERENCE: Harry A. Schmitz, Journal of Theoretics, Extensive Papers (2002). Paper includes three figures, one table and eight references.

Download: Journal of Theoretics Paper (pdf)


A Galilean Multiverse?: A Simple Physical Model of a Fractal Cosmos
By Harry A. Schmitz

A new model of a cosmos with hierarchical Universes depends on the existence of three-dimensional (3D) standing wave (SW) patterns of various ranks. Various aspects of this model are explored, both qualitatively and quantitatively, using simple geometries and simple physical concepts. The number of particles in our Universe is shown to equal the square of the ratio between the radius of the Universe and the effective radius of a particle. It is shown that a series of Universes terminates with our visible Universe.

REFERENCE: Harry A. Schmitz, Proceeding of the Natural Philosophy Alliance, International Conference, June 9-13, 2003, Journal of New Energy, vol. 7, No. 3, pp. 169-172, 2003, ISSN 1086-8259.

Download: NPA2003(pdf) • NPA2003 (ppt)


Mechanics of Particles in the Fractal Cosmos

By Harry A. Schmitz

A fractal particle is a three-dimensional (3D) standing wave (SW) superimposed on much smaller fractal particles, which comprise the finite substrate of one universe within an hierarchical series of fractal universes, or a fractal cosmos. In this presentation, units of absolute time and length are defined with respect to the frame of reference of a fractal universe. It is then shown that, for a fractal particle in motion, the frequency of vibration decreases (clock retardation) and the wavelength decreases in the direction of motion (length contraction) as the velocity of the particle increases with respect to the rest frame of (i.e., zero-velocity in) the fractal universe. Predictions are in agreement with experimental results, yet the equations of “fractal mechanics” are derived without recourse to the controversial two principles of Einstein's special relativity theory (SRT). The present derivation is based on Newtonian mechanics as applied to the built-in clocks and rulers of a fractal particle. It is indicated that Einstein's ad hoc derivation is preposterous and superfluous in the context of the fractal cosmos and leads to unnecessary paradoxes. In conclusion, the fractal cosmos hypothesis is compatible with experimental results relating to clock retardation and length contraction, suggesting that it is a robust theory worth examining in greater detail.

REFERENCE: Harry A. Schmitz, Proceedings of the Natural Philosophy Alliance, Vol. 1, No. 1, pp. 100-102, Spring 2004 (ISSN 1555-4775). Paper includes 12 references.

Download: NPA2004(pdf) • NPA2004(ppt)


Time Standards and Particle Interactions in a Fractal Universe, with Remarks on Gravity 

By Harry A. Schmitz

A fractal particle is a three-dimensional, standing-wave pattern. This paper examines how fractal particles can become shorter in wavelength and vibrate faster with the passage of time. ‘Absolute’ time is defined independently of particles, and hence is unchanging. ‘Relative’ time is based on the period of oscillation of fractal particles; it changes relative to the age of a fractal universe. In this paper, a simple, elegant equation is derived to correlate these two time standards, and calculate the age of our universe. I show here how particle interactions are possible: the standing wave around a source particle interacts with the maximum energy density at the core of a test particle, resulting in a redirection of energy, i.e., a force. For a test particle starting at rest, this electrostatic force increases the kinetic energy of the test particle. Repulsion between like-particles and attraction between unalike-particles is explained by the cylindrical or spherical symmetries of fractal particles. Gravitational attraction occurs because, as particle wavelengths become shorter with time, a portion of the energy stored around the test particle gradually is released in a way that causes an attractive force.

REFERENCE: Harry A. Schmitz, Proceedings of the Natural Philosophy Alliance, Vol. 3, No. 2, pp. 263-268, Tulsa 2006 (ISSN 1555-4775). Paper was delivered at Storrs NPA meeting in 2005. Paper includes 11 references.

Download: Paper (pdf)        Presentation (pdf)


The Physical and Philosophical Nature of the Universe

By Harry W. Schmitz

(Original manuscript published circa 1975.)

“It would be much more preferable to have a conflict in understanding reveal a fault in the concepts, rather than to have the conflict exist because of a misinterpretation of the full nature and scope of the concepts.”

— Harry Walter Schmitz, Glens Falls, New York, 1975.

REFERENCE: Harry W. Schmitz, “The Physical and Philosophical Nature of the Universe,” edited and with introduction by Harry A. Schmitz. Presently only the first seven chapters are available.

Download Book(pdf)



In the 1970s, Harry W. Schmitz wrote a treatise, modestly titled “The Physical and Philosophical Nature of the Universe,” in which he summarized the main results of his lifetime of research. He passed away suddenly in November 1979, a few weeks before his fifty-sixth birthday. He estimated that he was fifty years ahead of his time. He might be about right. After all, the times have changed. There is more talk than ever before of “multiverses” and dreams of a “unified field theory” or a “theory of everything” are still very much alive. The end of physics is nowhere in sight, yet it is widely acknowledged that not much more progress is possible without the introduction of radical ideas followed by a major paradigm shift.

Many of these ideas about the fractal cosmos originated more than 50 years ago with Harry Walter Schmitz (1923-1979). HWS served in the U.S. Army 12th Armored Division from December 1944 to May 1945 in France and Germany and was awarded the Bronze Star. He was graduated from Syracuse University in 1949 and worked as an engineer for the next 30 years obtaining eight patents. During that period, in his spare time, he extended and tested his theory against the theories and experimental results available to him. He left behind a considerable body of notes, including a remarkable treatise summarizing his major results.

HWS first attempted to teach his radical ideas to me approximately 35 years ago. My contribution here has been to simplify and generalize the model in part by describing some of the basic ideas in terms of a fractal object. I am grateful to my brother David Schmitz for his artistic rendition of several key concepts.

 – Harry A. Schmitz