Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
FractalIn mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.
Fractal curveA fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts.
Fractal analysisFractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science.
Pulmonary edemaPulmonary edema, also known as pulmonary congestion, is excessive liquid accumulation in the tissue and air spaces (usually alveoli) of the lungs. It leads to impaired gas exchange and may cause hypoxemia and respiratory failure. It is due to either failure of the left ventricle of the heart to remove oxygenated blood adequately from the pulmonary circulation (cardiogenic pulmonary edema), or an injury to the lung tissue directly or blood vessels of the lung (non-cardiogenic pulmonary edema).
Minkowski–Bouligand dimensionIn fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand. To calculate this dimension for a fractal , imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set.
Hausdorff dimensionIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension.
Fractal expressionismFractal expressionism is used to distinguish fractal art generated directly by artists from fractal art generated using mathematics and/or computers. Fractals are patterns that repeat at increasingly fine scales and are prevalent in natural scenery (examples include clouds, rivers, and mountains). Fractal expressionism implies a direct expression of nature's patterns in an art work. The initial studies of fractal expressionism focused on the poured paintings by Jackson Pollock (1912-1956), whose work has traditionally been associated with the abstract expressionist movement.
Pulmonary embolismPulmonary embolism (PE) is a blockage of an artery in the lungs by a substance that has moved from elsewhere in the body through the bloodstream (embolism). Symptoms of a PE may include shortness of breath, chest pain particularly upon breathing in, and coughing up blood. Symptoms of a blood clot in the leg may also be present, such as a red, warm, swollen, and painful leg. Signs of a PE include low blood oxygen levels, rapid breathing, rapid heart rate, and sometimes a mild fever.
X-rayX-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.
Chest radiographA chest radiograph, called a chest X-ray (CXR), or chest film, is a projection radiograph of the chest used to diagnose conditions affecting the chest, its contents, and nearby structures. Chest radiographs are the most common film taken in medicine. Like all methods of radiography, chest radiography employs ionizing radiation in the form of X-rays to generate images of the chest. The mean radiation dose to an adult from a chest radiograph is around 0.02 mSv (2 mrem) for a front view (PA, or posteroanterior) and 0.
CT scanA computed tomography scan (usually abbreviated to CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use a rotating X-ray tube and a row of detectors placed in a gantry to measure X-ray attenuations by different tissues inside the body.
RadiographyRadiography is an imaging technique using X-rays, gamma rays, or similar ionizing radiation and non-ionizing radiation to view the internal form of an object. Applications of radiography include medical radiography ("diagnostic" and "therapeutic") and industrial radiography. Similar techniques are used in airport security (where "body scanners" generally use backscatter X-ray). To create an image in conventional radiography, a beam of X-rays is produced by an X-ray generator and is projected toward the object.
High-altitude pulmonary edemaHigh-altitude pulmonary edema (HAPE) is a life-threatening form of non-cardiogenic pulmonary edema that occurs in otherwise healthy people at altitudes typically above . However, cases have also been reported between in more vulnerable subjects. Classically, HAPE occurs in persons normally living at low altitude who travel to an altitude above 2,500 meters (8,200 feet). Re-entry HAPE is also an entity that has been described in persons who normally live at high altitude but who develop pulmonary edema after returning from a stay at low altitude.
Pulmonary contusionA pulmonary contusion, also known as lung contusion, is a bruise of the lung, caused by chest trauma. As a result of damage to capillaries, blood and other fluids accumulate in the lung tissue. The excess fluid interferes with gas exchange, potentially leading to inadequate oxygen levels (hypoxia). Unlike pulmonary laceration, another type of lung injury, pulmonary contusion does not involve a cut or tear of the lung tissue. A pulmonary contusion is usually caused directly by blunt trauma but can also result from explosion injuries or a shock wave associated with penetrating trauma.
Pulmonary arteryA pulmonary artery is an artery in the pulmonary circulation that carries deoxygenated blood from the right side of the heart to the lungs. The largest pulmonary artery is the main pulmonary artery or pulmonary trunk from the heart, and the smallest ones are the arterioles, which lead to the capillaries that surround the pulmonary alveoli. The pulmonary arteries are blood vessels that carry systemic venous blood from the right ventricle of the heart to the microcirculation of the lungs.
RadiologyRadiology (,reidI'Ql@dZi ) is the medical discipline that uses medical imaging to diagnose diseases and guide their treatment, within the bodies of humans and other animals. It began with radiography (which is why its name has a root referring to radiation), but today it includes all imaging modalities, including those that use no electromagnetic radiation (such as ultrasonography and magnetic resonance imaging), as well as others that do, such as computed tomography (CT), fluoroscopy, and nuclear medicine including positron emission tomography (PET).
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
ImageAn image is a visual representation of something. An image can be a two-dimensional (2D) representation, such as a drawing, painting, or photograph, or a three-dimensional (3D) object, such as a carving or sculpture. An image may be displayed through other media, including projection on a surface, activation of electronic signals, or digital displays. Two-dimensional images can be still or animated. Still images can usually be reproduced through mechanical means, such as photography, printmaking or photocopying.
PathologyPathology is the study of the causes and effects of disease or injury. The word pathology also refers to the study of disease in general, incorporating a wide range of biology research fields and medical practices. However, when used in the context of modern medical treatment, the term is often used in a narrower fashion to refer to processes and tests that fall within the contemporary medical field of "general pathology", an area which includes a number of distinct but inter-related medical specialties that diagnose disease, mostly through analysis of tissue and human cell samples.
