How the generator works ?
Our generator is develloped under Javascript language, which is interpreted on client-side. So, performance and time of pic generation is plateform-depending. Using a client-side generator was chosen because it won't affect web server performance if a high traffic is done on our server. In others words, this method take profit from each client computers's performance.
Different types of algorithms
- Circle Based Algorithms : Those agorithms generates on a circle an amount of points with exactly the same angle, there is the initialisation. After that, and for a certain amount of iterations, the algorithm will choose if a point need to be generated, this is the difference between the 2 agorithms : the condition to allow a new point to be generated and displayed is different between them. Evidently, more are the amount of iterations, more the fractal will be developed into sub-layers, and more it will be precise. You need to increase the numbers of iterations if you want to get a precise fractal at high resolutions, because the generation is pixel by pixel.
- Barnsley Fern Algorithm : This algorithm uses four functions with matrices. Each function as a certain probability of being used. Each function takes to input (x and y position of the pixel) and as two output (x and y of the new position of the pixel). You can read more here : https://en.wikipedia.org/wiki/Barnsley_fern
- Mandelbrot Set : This algorithm use complex numbers and plot them on the complex plane. Each pixel coordonate is treated as a complex number and it's color is calculated based on the number of iteration it takes for a complex suit to tend to infinity, if it doesn't then it is considered as part of the background. You can read more here : https://en.wikipedia.org/wiki/Mandelbrot_set
Where you can find Fractals in environemment ?
Fractals are everywhere ! There's a lot of domains that where you can find fractals, as :
- Mathematics : fractals in mathematics are objects as surfaces or curves with the particularity that the structure is invariant as the scale changes.
- Biology and geology : lot of organisms, but also landforms and others things are fractals-like, as snowflakes, rivers, cauliflower, trees, fern and even blood vessels.
- Physics : the entire structure of universe can be represented as a fractal, others things as thunder are as well as a fractal.