Yes.
Fractals are a special kind of curve. They are space filling curves and have dimensions that are between those of a line (D = 1) and an area (D = 2).
Some common techniques for generating fractals would be to use iterated function systems, strange attractors, escape-time fractals, and random fractals.
There are infinitely many fractals so no list can exist.
Fractals were discovered in 1975 by a scientist names Benoit Mandelbrot.
Geometry and fractals are closely related, as fractals are geometric shapes that display self-similarity across different scales. While traditional geometry often focuses on shapes with defined dimensions and properties, fractals can have infinitely complex structures that challenge conventional notions of size and form. They are mathematically generated using recursive algorithms, highlighting the relationship between geometric principles and complex patterns found in nature. This connection illustrates how geometry can extend beyond simple shapes to encompass intricate, infinitely detailed structures.
No. Idealised objects have 0 or 1 dimensions. Day to day objects have 2 or 3 dimensions. More exotic objects have 4 or more integer dimensions and fractals have fractional dimensions.
They have positive non-integer dimensions.
Traditional geometric figures have dimensions which are integers: 0 for a point, 1 for a line or Mobius strip, 2 for a plane figure or Klein bottle, and 3 for a solid. Fractals have dimensions which are not integers.
Fractals are a special kind of curve. They are space filling curves and have dimensions that are between those of a line (D = 1) and an area (D = 2).
Any surface which is a fractals has a fractional dimension. But the value of the dimension is less than 2.
They can be three dimensional, for example, the Menger Sponge. Mathematically, there is no limit to the number of dimensions.
A fractal in a 2-dimensional plane has a dimension between 1 and 2.
Crystals are usually not fractals.
Pi is a number. There are no fractals of pi.
Nobody. Fractals are not owned by anyone!
The Beauty of Fractals was created in 1986.
Some common techniques for generating fractals would be to use iterated function systems, strange attractors, escape-time fractals, and random fractals.