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I was this summer at a lecture RMS held at a University in Athens and he said that gif format is patented. The banner is in gif format and not png. Should it be in png format or have I understood something wrong?

The Portable Network Graphics (PNG) format was designed to replace the older and simpler GIF format and, to some extent, the much more complex TIFF format. (See the main page or the history page for background information.) Here we'll concentrate on two major uses: the World Wide Web (WWW) and image-editing.

For the Web, PNG really has three main advantages over GIF: alpha channels (variable transparency), gamma correction (cross-platform control of image brightness), and two-dimensional interlacing (a method of progressive display). PNG also compresses better than GIF in almost every case, but the difference is generally only around 5% to 25%, not a large enough factor to encourage folks to switch on that basis alone. One GIF feature that PNG does not try to reproduce is multiple-image support, especially animations; PNG was and is intended to be a single-image format only. (A very PNG-like extension format called MNG was finalized in mid-1999 and is beginning to be supported by various applications, but MNGs and PNGs will have different file extensions and different purposes.)

For image editing, either professional or otherwise, PNG provides a useful format for the storage of intermediate stages of editing. Since PNG's compression is fully lossless--and since it supports up to 48-bit truecolor or 16-bit grayscale--saving, restoring and re-saving an image will not degrade its quality, unlike standard JPEG (even at its highest quality settings). And unlike TIFF, the PNG specification leaves no room for implementors to pick and choose what features they'll support; the result is that a PNG image saved in one app is readable in any other PNG-supporting application. (Note that for transmission of finished truecolor images--especially photographic ones--JPEG is almost always a better choice. Although JPEG's lossy compression can introduce visible artifacts, these can be minimized, and the savings in file size even at high quality levels is much better than is generally possible with a lossless format like PNG. And for black-and-white images, particularly of text or drawings, TIFF's Group 4 fax compression or the JBIG format are often far better than 1-bit grayscale PNG.)
http://www.libpng.org/pub/png/pngintro.html