One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side …

It is based on a complex number equation (z n+1 = z n2 + c) which is repeated until it: Click and make a rectangle to zoom in, shift-click to zoom out. Click Options for more settings. This is a famous fractal …

Generate 25 iterations of any fractal in 2D. Switch between the main set, and its julia sets. Distance for testing divergence. Explore math with our beautiful, free online graphing calculator. Graph functions, …

Jul 23, 2025 · Fractals are generated using recursive mathematical formulas that define the structure and pattern of the fractal. The basic fractal formula involves iterating a function repeatedly, often with …

Oct 31, 2023 · You can create fractals with mathematical equations and algorithms, but there are also fractals in nature. At their most basic, fractals are a visual expression of a repeating pattern or …

Sep 12, 2020 · To find the dimension D of a fractal, determine the scaling factor S and the number of copies C of the original shape needed, then use the formula D = log (C) log (S)

Given a function f, like f x = x 2, the corresponding Julia set K f is a subset of all points in the complex plane, where the sequence formed by repeatedly applying f does not diverge. In many cases, the …

Finally, let's examine the "Magnet" fractal, which is particularly interesting, because it comes from an equation in physics that describes the way in which metals such as iron can gain or lose their …

So, you might be asking what exactly is a fractal? Well, a fractal, by definition, is a curve or geometric figure, each part of which has the same statistical character as the whole.

3 days ago · A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline …