The beauty of fractals

Let’s enjoy the mandlebrot first:










Even 2000 times magnification of the Mandelbrot set uncovers fine detail resembling the full set.




If you are interested some history and information:

The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Gottfried Leibnizconsidered recursive self-similarity.
It was not until 1872 that a function appeared whose graph would today be considered fractal.

Iterated functions in the complex plane were investigated in the late 19th and early 20th centuries by Henri Poincaré, Felix Klein, Pierre Fatou and Gaston Julia. Without the aid of modern computer graphics, however, they lacked the means to visualize the beauty of many of the objects that they had discovered.

In the 1960s, Benoît Mandelbrot started investigating self-similarity, in 1975 Mandelbrot coined the word "fractal" to denote an object whose Hausdorff–Besicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computer-constructed visualizations. These images captured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term "fractal".

Learning stages ...

Theory: There are four states of consciousness and competence that you may pass through as you learn.

Unconscious incompetence
As an unconscious incompetent, you do not know what you do not know. You are lack knowledge and skills in the area in question and are unaware of this lack.
In this state, you can exist for a very long time.

Conscious incompetence
As a conscious incompetent, you realize that you are not as expert as perhaps you thought you were or thought you could be.

Conscious competence
Becoming consciously competent often takes a while, as you steadily learn about the new area, either through experience or more formal learning.

Unconscious competence
Eventually you reach a point where you no longer have to think about what you are doing, and are competent without the significant effort that characterizes the state of conscious competence.

Cold and beautiful

Winter can be cold and beautiful as in this lane:



Morning light and fog that drifts by:





Some of the only greenery’s at this time of the year:

Start

I start this new year 2011 with a new blog .... let's see if I can make it interesting and with lots of variety.