Fractal geometry of nature (bone) may inspire medical devices shape

Medical devices, as orthopaedics prostheses and dental implants, have been designed over years on the strength of mechanical, clinical and biological indications. This sequence is the commonly accepted cognitive and research process: adapting the device to the surrounding environment (host tissue). Inverting this traditional logical approach, we started from bone microarchitecture analysis. Here we show that a unique geometric rule seems to underlie different morphologic and functional aspects of human jaw bone tissue: fractal properties of white trabeculae in low quality bone are similar to fractal properties of black spaces in high quality bone and vice versa. These data inspired the fractal bone quality classification and they were the starting point for reverse engineering to design specific dental implants threads. We introduce a new philosophy: bone decoding and with these data devices encoding. In the future, the method will be implemented for the analysis of other human or animal tissues in order to project medical devices and biomaterials with a microarchitecture driven by nature

Microscopic model of diffusion limited aggregation and electrodeposition in the presence of levelling molecules

A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions'' diffuse at random from the top of a container until encountering a cluster in contact with the bottom, to which they stick. The model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules which unbind atoms from the aggregate transforms the deposit to a 100% dense one (in 3D). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called ``leveller'' molecules which are used in electrochemical deposition

The Fractal Geometry of Grand Rapids

The fractal nature of cities\u27 geometry has been widely studied. By analyzing a city\u27s fractal pattern, we can obtain its fractal dimension, or measure of how complex it is. We will create models on how Grand Rapids\u27 complexity changed since its inception, and use those models to predict what the complexity is like today

The Fractal Dimension as Alternative Theoretical Tool to Examine and Develop Urban Patterns

Contemporary theories on urbanism admit the complex nature of the urban fabric. This means that reading and understanding urban facts requires a much more complex theoretical model than the Euclidian Geometry can offer. As Nikos Salingaros admits, we need to rethink the discipline of urbanism by involving algorithms as advanced developing tools. Urban patterns are produced by complex algorithms which describe their morphology and not just their geometry in Vitruvian terms. Especially in vernacular (self-grown) patterns is noted the presence of fractal algorithms as urban fabric generators. This research intends to identify and evaluate the fractal nature of Korça’s vernacular pattern by using the fractal dimension as measurement tool. By observing Korça’s pattern is easy to note the phenomena of the self-similarity and of a morphological hierarchy transmitted across the scales. Through a multi-scale analysis this research aims to verify the hypothesis of the fractal nature of this pattern. The self-affinity phenomena will be explored in the repetitive presence of specific planar motifs in different urban scales. Theoretically, the fractal dimension controls the dispersion of mass over a structure and in this case it gives information about the fragmentation scale of the build environment. The measurement process is done by the use of the box-counting method and the Fractalyse software. On one hand the research identifies the fractal nature of a self-grown pattern; on the other one it raises an important question: Can we list the fractal dimension as an additional parameter which gives more complete information about the urban morphologies

Geometric properties of two-dimensional O(n) loop configurations

We study the fractal geometry of O($n$) loop configurations in two dimensions by means of scaling and a Monte Carlo method, and compare the results with predictions based on the Coulomb gas technique. The Monte Carlo algorithm is applicable to models with noninteger $n$ and uses local updates. Although these updates typically lead to nonlocal modifications of loop connectivities, the number of operations required per update is only of order one. The Monte Carlo algorithm is applied to the O($n$) model for several values of $n$, including noninteger ones. We thus determine scaling exponents that describe the fractal nature of O($n$) loops at criticality. The results of the numerical analysis agree with the theoretical predictions.Comment: 18 pages, 6 figure

Fractals, Materials and Energy Technologies

World’s perennial need for energy yields the whole spectra of technological challenges and scientific tasks. An important stream in finding new solutions leads over materials characterized by precise microstructural architecture based on fractal geometry/analysis covering wide size ranges down to nano scale. Having such a deep geometric hierarchy opens new possibilities in energy storage capacities supported by fractal resources. These novel ideas are natural continuation of some early fractal applications have been used as a tool in energy research, applying on diverse energy technologies, from photovoltaics to fuel cells and carbon capture. All three items that are essential regarding energetic questions, free energy stocks location, energy harvesting and short/ long term energy storage have their specific common points with fractal nature. Also, the concept of energy as physical objects property, share some features characteristic to fractal objects. In other words, fractal, as a crucial concept of modern theoretical-experimental physics is tightly connected with the process of cultivating the wild energy as well. Here, the above items will be discussed. The term “geometry” as it is custom in plain language, understands “shape” rather than the science of geometry. In this sense, “geometry” describes property of hierarchy that is more present in every day’s life than we are usually aware of. Just note that all our senses often convey information on the quality of some matter by absorbing certain hierarchical order. The touch feeling of smooth or rough surface, olfactory or taste data differ by energetic level that generates according to geometry of particles or clusters that follow fractal patterns. Adjusting specific, a priori constructed fractal micro or nano architecture make the energetic flow more effective by decrease losses made by non-conformal geometry