Fractal, in mathematics, any of a class of complex geometric shapes that commonly have “fractional dimension ,” a concept first introduced by the mathematician Felix Hausdorff in 1918. Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.
Is recursion a fractal?
If you can say “It’s a line!” then it’s not a fractal. Another fundamental component of fractal geometry is recursion. Fractals all have a recursive definition . We’ll start with recursion before developing techniques and code examples for building fractal patterns in Processing.
What does a fractal have to do with recursion?
Recursion is the process of repeating items in a self-similar way. It can be implemented in Scratch by making a Custom block that runs itself . This can be used to create Fractals. A fractal is pattern that produces a picture, which contains an infinite amount of copies of itself.
Is Sierpinski triangle a fractal?
The Sierpinski triangle is a self-similar fractal . It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area. Wacław Franciszek Sierpiński (1882 – 1969) was a Polish mathematician.
What is the purpose of fractals?
Why are fractals important? Fractals help us study and understand important scientific concepts , such as the way bacteria grow, patterns in freezing water (snowflakes) and brain waves, for example. Their formulas have made possible many scientific breakthroughs.
Is a fractal an algorithm?
I think you might not see fractals as an algorithm or something to program. Fractals is a concept! It is a mathematical concept of detailed pattern repeating itself . Therefore you can create a fractal in many ways, using different approaches, as shown in the image below.
Is Mandelbrot recursive?
The Mandelbrot Set is a beautiful example of the power of recursion . The function involved is extremely simple — so simple that you learned it in elementary school. ... After only three iterations, the function’s iteration on itself has formed an exponential curve of sorts.
What is the most famous fractal?
Largely because of its haunting beauty, the Mandelbrot set has become the most famous object in modern mathematics. It is also the breeding ground for the world’s most famous fractals.
Is lightning a fractal?
Similar to many shapes in nature, lightning strikes are fractals . ... It occurs when two or more strokes of lightning travel somewhat different paths. Forked lightning can go from cloud-to-ground, cloud-to-cloud, or cloud-to-air.
What are 3 well known fractals?
Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge , are some examples of such fractals.
Is the Triforce a fractal?
The Sierpiński triangle (sometimes spelled Sierpinski), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
Why is Sierpinski’s Triangle a fractal?
The Sierpinski triangle is a fractal described in 1915 by Waclaw Sierpinski. It is a self similar structure that occurs at different levels of iterations , or magnifications. ... This pattern is then repeated for the smaller triangles, and essentially has infinitely many possible iterations.
Why is Sierpinski triangle important?
This idea of triangular similarity is especially important in the case of the gasket because if we realize that each subtriangle of the gasket is, itself, actually another gasket with the same relative properties as the original gasket .
Is Fibonacci a fractal?
The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal .
How do we use fractals in everyday life?
Fractal mathematics has many practical uses, too – for example, in producing stunning and realistic computer graphics , in computer file compression systems, in the architecture of the networks that make up the internet and even in diagnosing some diseases.
Are humans fractals?
We are fractal . Our lungs, our circulatory system, our brains are like trees. They are fractal structures. ... Most natural objects – and that includes us human beings – are composed of many different types of fractals woven into each other, each with parts which have different fractal dimensions.
