 | |
| Original author(s) | Karl Runmo |
|---|---|
| Stable release | 2.11.1 |
| Size | 1.03 MiB |
| Available in | English |
| Type | Fractal-generating software |
| License | GNU AFFERO GENERAL PUBLIC LICENSE (fork) |
| Website | www |
Kalles Fraktaler is a free Windows-based fractal zoom computer program used for zooming into fractals such as the Mandelbrot set and the Burning Ship fractal at very high speed, utilizing Perturbation and Series Approximation. [1]
Kalles Fraktaler focuses on zooming into fractals. This is possible in the included fractal formulas such like the Mandelbrot set, Burning ship or so called "TheRedshiftRider" fractals. Many tweaks can visualize phenomena better or solve glitches concerning the calculation issues. Other functions are color seeds, slopes for showing iteration depths or entering location parameters in the complex plane. The via zooming reached location can be saved as a KFR file. The rendered image can be saved or be a part of a zoom sequence, which can be later used for a fractal zoom video.
The program got forked to Kalle's Fraktaler 2+ with additional functions. The newest release is 2.15.1.6 from 2020/12/08 (December 12, 2020). The license is AGPLv3+. [2]
Many features offered by the fork of Kalles Fraktaler can be confusing to use, or take hours to deduce their purpose. Below are a few helpful tips and tricks to maximize the quality of your images and videos.
Many in-depth tutorials exist on Youtube, which can be accessed by searching "Kalles Fraktaler tutorial
Benoit B.Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
In 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 geometry lies within the mathematical branch of measure theory.
The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not diverge to infinity when iterated starting at , i.e., for which the sequence , , etc., remains bounded in absolute value.
In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed.
Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still digital images, animations, and media. Fractal art developed from the mid-1980s onwards. It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at the intersection of generative art and computer art. They combine to produce a type of abstract art.
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic".
The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. Its name reflects its pareidolic resemblance to classical depictions of Gautama Buddha, seated in a meditation pose with a forehead mark (tikka), a traditional oval crown (ushnisha), and ringlet of hair.
Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. An "epsilon cross" is a cross-shaped orbit trap.
The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(z) ∈ [z] or transcendental function. It is the Julia set of the meromorphic function z ↦ z − p(z)/p′(z) which is given by Newton's method. When there are no attractive cycles (of order greater than 1), it divides the complex plane into regions Gk, each of which is associated with a root ζk of the polynomial, k = 1, …, deg(p). In this way the Newton fractal is similar to the Mandelbrot set, and like other fractals it exhibits an intricate appearance arising from a simple description. It is relevant to numerical analysis because it shows that (outside the region of quadratic convergence) the Newton method can be very sensitive to its choice of start point.
The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:
The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal curve–like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox of length" was previously noted by Hugo Steinhaus, the first systematic study of this phenomenon was by Lewis Fry Richardson, and it was expanded upon by Benoit Mandelbrot.
Newt is a programming library for color text mode, widget-based user interfaces. Newt can be used to add stacked windows, entry widgets, checkboxes, radio buttons, labels, plain text fields, scrollbars, etc., to text user interfaces. This package also contains the shared library needed by programs built with newt, as well as a CLI application whiptail, which provides the most commonly used features of dialog. Newt is based on the slang library. It abbreviates from Not Erik's Windowing Toolkit.
In mathematics, the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping instead of used for the Mandelbrot set. It was introduced by W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark. John Milnor found tricorn-like sets as a prototypical configuration in the parameter space of real cubic polynomials, and in various other families of rational maps.
XaoS is an interactive fractal zoomer program. It allows the user to continuously zoom in or out of a fractal in real-time.
Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both free and commercial. Mobile apps are available to play or tinker with fractals. Some programmers create fractal software for themselves because of the novelty and because of the challenge in understanding the related mathematics. The generation of fractals has led to some very large problems for pure mathematics.
Sterling is a fractal-generating computer program written in the C programming language in 1999 for Microsoft Windows by Stephen C. Ferguson. Sterling is now freeware while Sterling2 is a freeware version of Sterling with different algorithms. It was released in September 2008 by Tad Boniecki. Apart from the name, the program looks just like the original Sterling. The only internals that are different are the 50 formulae for fractal generation. Parameter files made by Sterling can be used in Sterling2 and vice versa, though they will draw different images.
In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions. It is typically drawn in three dimensions for illustrative purposes.
Ultra Fractal is a fractal generation and rendering software application. The program was the first publicly available fractal software which featured layering methods previously only found in image editing software. Because of this, the program has become popular for use in the creation of fractal art.
An ordinary fractal string is a bounded, open subset of the real number line. Such a subset can be written as an at-most-countable union of connected open intervals with associated lengths written in non-increasing order; we also refer to as a fractal string. For example, is a fractal string corresponding to the Cantor set. A fractal string is the analogue of a one-dimensional "fractal drum," and typically the set has a boundary which corresponds to a fractal such as the Cantor set. The heuristic idea of a fractal string is to study a (one-dimensional) fractal using the "space around the fractal." It turns out that the sequence of lengths of the set itself is "intrinsic," in the sense that the fractal string itself contains information about the fractal to which it corresponds.
There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently.
 | This Microsoft Windows software-related article is a stub. You can help Wikipedia by expanding it. |