**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 x^{2}+y^{2}.
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 x 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**