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Fractals are complex geometric shapes that exhibit self-similarity at different scales, meaning that the same patterns and structures can be found at different levels of magnification.

New creation on youtube. Drumfunk music with "Frogtal" fractal.
02/10/2024

New creation on youtube. Drumfunk music with "Frogtal" fractal.

In 1861, the mathematical community was astounded by the discovery of the world's first fractal. Karl Weierstrass, a German mathematician, crafted a jagged z...

https://www.youtube.com/watch?v=MrEHbPK4DEk
02/09/2024

https://www.youtube.com/watch?v=MrEHbPK4DEk

Get ready to unleash your inner energy with "Feel Alive Again" album – a high-octane blend of aggressive heavy metal, orchestral intensity, and epic cinemati...

Fractal Animation
10/08/2024

Fractal Animation

Website: https://puhapro.com ------------------------------------------ ...

I hope you will like it
10/08/2024

I hope you will like it

Welcome to the whimsical world of fractals in nature! Ever wondered why the veins on a leaf look suspiciously like the rivers on a map, or why a cauliflower ...

Wearable Fractal Art.
13/07/2024

Wearable Fractal Art.

Wearable Fractal Art.

https://youtu.be/yqq_oWgngSg
30/05/2024

https://youtu.be/yqq_oWgngSg

This fractal animation showcases an intricate garland of vibrant hues, characterised by sudden movement that brings the patterns to life. Dominated by purple...

02/04/2024
Fractals are incredibly interesting shapes with many complex qualities that cannot be seen anywhere else in mathematics ...
11/03/2024

Fractals are incredibly interesting shapes with many complex qualities that cannot be seen anywhere else in mathematics or nature. Due to their unique qualities and potential in various scientific disciplines, studying them is an important part of understanding natural processes and optimizing numerous equations and simulations.

# fractals

In terms of science, fractals have many applications across various disciplines such as signals and image analysis, comp...
09/03/2024

In terms of science, fractals have many applications across various disciplines such as signals and image analysis, computer networks, and biology.

The study of fractals is particularly important in geometrical engineering fields such as architecture and civil engineering due to their irregular forms providing a more efficient use of materials than traditional shapes like squares or rectangles.

Fractals also help to describe physical phenomenon such as diffusion-limited aggregation (DLA) where particles randomly gather around one central point taking up an intricate shape created by a fractal pattern.

Fractals occupy a special place in mathematics and science. In mathematics, fractals are objects of study because of the...
06/03/2024

Fractals occupy a special place in mathematics and science. In mathematics, fractals are objects of study because of the unique properties they possess.

Fractals are complex and intriguing mathematical shapes, often characterized by repeating patterns that branch off in al...
27/02/2024

Fractals are complex and intriguing mathematical shapes, often characterized by repeating patterns that branch off in all directions. Examples of fractal shapes can be found everywhere in nature.

Fractals are complex and intriguing mathematical shapes, often characterized by repeating patterns that branch off in al...
26/02/2024

Fractals are complex and intriguing mathematical shapes, often characterized by repeating patterns that branch off in all directions. Examples of fractal shapes can be found everywher in nature.

Helge von Koch's snowflake curve is a well-known fractal that is generated by a simple recursive algorithm. The snowflak...
22/02/2024

Helge von Koch's snowflake curve is a well-known fractal that is generated by a simple recursive algorithm. The snowflake curve is a variation of the Koch curve, which is generated by adding triangular "arms" to each line segment of the previous iteration.
To generate the snowflake curve, we start with an equilateral triangle, and then replace each line segment with four smaller segments, forming a smaller equilateral triangle at each corner. We then repeat this process recursively, replacing each line segment with a new set of smaller line segments, until we have a curve that looks like a snowflake.
The snowflake curve has several interesting properties. First, it is a self-similar shape, meaning that it looks the same at different scales. Specifically, if we zoom in on any part of the curve, we will see smaller versions of the same pattern repeated over and over again.
Second, the snowflake curve has an infinite perimeter but a finite area. This is because the length of the curve increases without bound as we iterate the algorithm, but the total area enclosed by the curve converges to a finite value.
Finally, the snowflake curve has a fractal dimension of approximately 1.26, which is a non-integer value that captures the complex and irregular nature of the shape.
The snowflake curve is a classic example of a fractal, and it has been used in many applications, such as computer graphics, digital imaging, and the study of complex systems. It is also a popular subject in recreational mathematics and art, due to its intricate and visually striking patterns.

Fractals possess several unique characteristics: 1. Self-similarity:  They exhibit self-similarity, displaying a repeati...
06/02/2024

Fractals possess several unique characteristics:

1. Self-similarity: They exhibit self-similarity, displaying a repeating pattern that is visible at any level of magnification.
2. Irregularity: Their shapes are irregular and lack the symmetry of traditional geometric shapes.
3. Dimensionality: They are described as having fractional dimensions, existing between two-dimensional and three-dimensional shapes.
4. Complexity: They are highly complex, with intricate details that can be seen at any level of magnification.
5. Scale invariance: They are scale invariant, appearing the same regardless of the level of magnification applied to them.

The Geometry of Fractals The geometry of fractals is a complex and fascinating subject. Fractals are shapes that are sel...
02/02/2024

The Geometry of Fractals

The geometry of fractals is a complex and fascinating subject. Fractals are shapes that are self-similar, meaning they have the same structure at different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. This process is known as iteration, and it produces a never-ending pattern of intricate detail. The most famous example of a fractal is the Mandelbrot set, which was discovered by mathematician Benoit Mandelbrot in 1980. It is a two-dimensional shape that has infinitely complex boundaries, making it impossible to measure its area or perimeter.

For years, mathematicians had been studying the key concepts associated with fractals and many examples, such as the Koch or “snowflake” curve, were already known. However, it was not until Mandelbrot introduced fractals in 1975 that their potential as a tool for applied mathematics was recognized. This new system of geometry has since had a considerable influence on physical chemistry, physiology, fluid mechanics and other areas.

Applications of FractalsFractals are fascinating mathematical objects that have been studied and explored by scientists ...
29/01/2024

Applications of Fractals
Fractals are fascinating mathematical objects that have been studied and explored by scientists and artists alike.

They are infinitely complex patterns that repeat at different scales, and they have many applications in the world of science and art. From computer graphics to data compression to chaos theory, fractals have been used to explore a wide range of topics.

In computer graphics, fractals are used to create intricate and realistic images. By using fractal algorithms, computer graphics artists can create landscapes, trees, and other natural elements with remarkable detail. This technique is often used in video games and animated films to create realistic environments.

Data compression is another application of fractals. By using fractal algorithms, data can be compressed into a much smaller size without losing any of its information content. This makes it easier to store large amounts of data on computers or other digital devices.

Fractals have also been used in chaos theory. Chaos theory is the study of unpredictable systems, such as weather patterns or stock markets. By studying the patterns created by fractals, scientists can gain insight into how these systems behave and make predictions about their future behaviour.

Overall, fractals are an incredibly powerful tool for exploring a variety of topics in science and art. From computer graphics to data compression to chaos theory, fractals have been used to gain insight into complex systems and create stunning works of art.

Properties of Fractals 1. Self-similarity: Fractals often display a repeating pattern that is visible at any level of ma...
26/01/2024

Properties of Fractals

1. Self-similarity: Fractals often display a repeating pattern that is visible at any level of magnification.
2. Irregularity: Fractals are typically irregular in shape, meaning they lack the symmetry of traditional geometric shapes.
3. Dimensionality: Fractals are often described as having fractional dimensions, meaning they exist between the traditional two-dimensional and three-dimensional shapes.
4. Complexity: Fractals are often highly complex, with intricate details that can be seen at any level of magnification.
5. Scale invariance: Fractals are often scale invariant, meaning they look the same regardless of the level of magnification.

Free fractal. Download free.
10/10/2021

Free fractal. Download free.

Free to download. Mandelbulb3D fractal.
01/09/2021

Free to download. Mandelbulb3D fractal.

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