First of all fractal is a geometrical shape. In general terms it's a geometrical shape shat when subdivided breaks into parts that are a reduced copy of the original. Well these reduced copies can approximately represent the main, that these copies constitute. Self similarity is the main them in fractals. Or else a it can also be said that a fractal shape is it self made of smaller copies of it self. Or in other terms they have Scale Invariance. What does this scale invariance mean? Well it's a feature of geometry of an object that tells that the shape of the object does not change over dimensions of length. Fractals can also be thought of as figures with infinite amount of details. When magnified they still represent the same geometry. Fractals have the following property
1. It has a fine structure at arbitrarily small scales.
2. It is too irregular to be easily described in traditional Euclidean geometric language.
3. It is self-similar (at least approximately or stochastically).
4. It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
5. It has a simple and recursive definition.
The mathematics behind fractals began to take shape in the 17th century when philosopher Leibniz considered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense).
It took until 1872 before a function appeared whose graph would today be considered fractal, when Karl Weierstrass gave an example of a function with the non-intuitive property of being everywhere continuous but nowhere differentiable.
Now with these properties and math we will go on later, first of all we will concentrate on the details of generating them as this blog is not about fractals; rather it's about how to generate designs. I will create a few fractals and post them here, so that all can try. As I was telling I was planning to use only POV-Ray, but now am planning to use OpenGl also. So I will post them tomorrow.
1. It has a fine structure at arbitrarily small scales.
2. It is too irregular to be easily described in traditional Euclidean geometric language.
3. It is self-similar (at least approximately or stochastically).
4. It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
5. It has a simple and recursive definition.
The mathematics behind fractals began to take shape in the 17th century when philosopher Leibniz considered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense).
It took until 1872 before a function appeared whose graph would today be considered fractal, when Karl Weierstrass gave an example of a function with the non-intuitive property of being everywhere continuous but nowhere differentiable.
Now with these properties and math we will go on later, first of all we will concentrate on the details of generating them as this blog is not about fractals; rather it's about how to generate designs. I will create a few fractals and post them here, so that all can try. As I was telling I was planning to use only POV-Ray, but now am planning to use OpenGl also. So I will post them tomorrow.
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