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...
Fractal figures generated using L-systems