https://en.wikipedia.org/wiki/Fractal
A fractal is a geometric shape with detailed structure at arbitrarily small scales, often having a fractal dimension exceeding its topological dimension. Learn about the origin, characteristics, techniques, and uses of fractals in mathematics, nature, art, and technology.

https://brilliant.org/wiki/fractals/
Learn what fractals are, how they arise from self-similar patterns and iterated rules, and how to measure their dimensions. Explore fractals in geometry, algebra, and nature with interactive diagrams and exercises.

https://fractalfoundation.org/resources/what-are-fractals/
Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Learn more about fractals, chaos theory, and how they relate to nature and mathematics.

https://science.howstuffworks.com/math-concepts/fractals.htm
Learn what fractals are, how they are created, and why they are important in math and nature. Explore the history, terminology, and examples of fractals, from the Mandelbrot set to the Koch snowflake.

https://www.britannica.com/science/fractal
A fractal is a complex geometric shape with fractional dimension and self-similarity. Learn about the history, properties, and uses of fractals in mathematics, nature, and art from Britannica.

https://www.newscientist.com/article/mg26234921-400-what-are-fractals-and-how-can-they-help-us-understand-the-world/
Fractals are common in nature because of the surprisingly simple way they are made. Mathematically, they also help us make sense of complexity and chaos - and maybe even quantum weirdness. You

https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/07%3A_Mathematics_and_the_Arts/7.04%3A_Fractals
Learn what fractals are, how they are created by recursion, and how they exhibit self-similarity and dimensional properties. Explore the Sierpinski gasket, the Koch curve, and other fractals with interactive applets and exercises.

https://theconversation.com/explainer-what-are-fractals-10865
Fractals are complex and intricate shapes that occur in nature and mathematics. Learn about their four key features: infinite intricacy, zoom symmetry, complexity from simplicity and fractional dimensions.

https://mathigon.org/course/fractals/introduction
Learn what fractals are and how they occur in nature and mathematics. Explore examples of fractals such as the Sierpinski triangle, the Mandelbrot set, and space filling curves.

https://www.allmath.com/geometry/fractal-geometry
Learn what fractals are, how they exhibit self-similarity, and how they are classified into three types: self-similar, self-affine, and invariant. Explore examples of fractals such as the Sierpinski triangle and the Mandelbrot set, and see how they are used in computer graphics and data compression.

https://mathworld.wolfram.com/Fractal.html
A fractal is a self-similar object or quantity that has the same "type" of structures on all scales. Learn about the fractal dimension, the coastline paradox, and the prototypical fractals such as the Mandelbrot set and the Koch snowflake.

https://worldscientific.com/worldscinet/fractals
Fractals often start with a simple geometrical object and a rule for changing the object that leads to objects that are so complex that their dimension is not an integer. According to Michael Frame, Benoit Mandelbrot (who first coined the word "fractal" and was the founding editor of this journal) considered himself above all a storyteller.

https://www.khanacademy.org/partner-content/mit-k12/mit-k12-math-and-engineering/mit-math/v/what-is-a-fractal-and-what-are-they-good-for
Learn what fractals are, how they are created by repeating mathematical equations, and how they can be found in nature and technology. Watch a video and see examples of fractals such as the Koch snowflake, the Menger sponge, and the Sierpinski triangle.

https://www.youtube.com/watch?v=WFtTdf3I6Ug
Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, a undergrad in Math at MIT, delves into their mysterious pro

https://www.youtube.com/watch?v=w_MNQBWQ5DI
What is a fractal, and how can fractals help us understand the universe? Classic examples of fractals in nature are broccoli and snowflakes. They can offer a

https://math.libretexts.org/Courses/Rio_Hondo/Math_150%3A_Survey_of_Mathematics/06%3A_Measurement_and_Geometry/6.03%3A_Fractals/6.3.01%3A_Fractal_Dimension
Learn how to calculate the dimension of a fractal using the scaling-dimension relation and logarithms. See examples of fractals with different dimensions, such as the Sierpinski gasket and the Koch snowflake.

https://www.treehugger.com/amazing-fractals-found-in-nature-4868776
Learn how fractals, geometric shapes that display similarity through different scales, are ubiquitous in nature. Discover examples of fractals in plants, animals, minerals, and water, and how they optimize their functions and forms.

https://www.gleammath.com/post/fractals
Fractals are patterns that exist somewhere between the finite and infinite. As we'll see, they even have fractional dimensions (hence the name fractal) because they exist somewhere between integer dimensions! We'll look at how these seemingly impossible shapes exist when we allow ourselves to extend to infinity, in the third part of my inf

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/15%3A_Fractals
Learn about fractals, mathematical sets that exhibit self-similarity and dimensional properties. Explore examples of fractals, such as the Sierpinski gasket, the Mandelbrot set, and complex recursive sequences.

https://iternal.ai/what-is-a-fractal/
Fractals can actually have fractional dimensions, like for example 2.5 dimensions. A great way to explain dimensionality is thinking of it as a measure of roughness, or how well does a given shape fill the space around it. A sphere for example fills 3 dimensions of space because it is a solid object. A piece of paper fills 2 dimensions of space.

https://encyclopediaofmath.org/wiki/Fractals
Fractals are point sets with non-integer dimension that are self-similar or quasi-self-similar. Learn about the history, definitions, examples and applications of fractals in mathematics and physics.

https://www.bbvaopenmind.com/en/science/mathematics/fractals-natures-geometric-code/
Fractals: Nature's Geometric Code. Pythagoras' theorem, the formulas for calculating the surface area and volume of geometric shapes, the number pi…These are all concepts of classical or Euclidean geometry taught in schools, alongside analytic geometry (which translates these figures into algebraic expressions such as functions or

https://fractalfoundation.org/resources/
First, we recommend you download the amazing, FREE fractal explorer, XaoS, which lets you zoom into mathematical fractals. When you create a really beautiful fractal, please enter it in the Fractal Challenge! (Elementary, middle & high school students only.) Next, explore the Fractivities page which features many different projects to do at