Wall paper

an applet made by António Miguel de Campos (Portugal

ERRORS DUE TO FINITE PRECISION IN COMPUTERS

 
When the fraccionary part of a number exceeds the possible precision, it is necessary to truncate the least significant digits. The result is similar to ingnoring the fractionary part of a real number.
Considering x and y, the screen coordinates, with values from -10 till a chosen value (inicially 110), we calculate the value of x2+y2. Then we take the larger integer smaller than that sum and use it to choose the color (1 of the 8 colors) of the corresponding pixel in screen.
If you select Show Error, you will see the value of the difference between each sum and the value of the larger integer smaller than that sum.

If you select 1-color tones, the program uses 8 colors which correspond to 8 different tones of the same «color».

The values of the 2 textfields on the right, after a division by 10, are used as the powers of x e y in the sum. Initially they are x^ 20 + y ^ 20, which corresponds to x2+y2. You can try to change some of these values...

If you choose values from -10 to 230 and 1-color tones and Show Value (the buttons will then read 8 colors and Show Error) and using values for x^ of 4, 8, 16 and 21 and for y^ of 8, for instance, you will see some interesting patterns...

 

Lorenz atractor - the butterfly effect in a strange atractor  

Fractal figures generated using L-systems 

Mandelbrot set and Julia sets