Fractal Art Project
Hint: Click the Fractal above to view a full size version of it
What are Fractals?
Fractals are complex geometric shapes in which a pattern repeats when zoomed in. These images will repeat with the pattern repeating the self-similar objects zooming into infinity. The resulting amzing image produced by continually zooming in is a fractal.
How are Fractals generated?
Fractals are generated from a starting point, the axiom, being transformed through a transformation. Each image undergoes infinite iterations, which creates the infinite repeating pattern seen when zooming in on a fractal image.
What do the assigned colors in the fractals mean?
The color is just a way to visualize the different areas of the fractal. Where there is black, zero continues being returned from the function (the cool art isn't present there). However, where the plethora of colors are, is where there are infinite possibility when the function keeps repeating, the range being plugged in to the original function. This shows the speed of each part of the fractal and how each part continues to repeat into infinity.
What is chaos in mathematics?
Chaos is when the norms are broken in dynamic sets, exhibiting a random sense, such as when things grow exponentially. It is hard to predict after a lot of growth and iterations have occured. Such things have been referred to as, chaotic.
How do fractals relate to chaos and complex numbers?
Fractals are chatoic images, theyappear as if theydo not follow anypattern, even though they are iterations of complex numbers. (Complex numbers are a+bi where there is a real number and an imaginary number). These fractals are generated when they are complex numbers undergo infinite iterations.