I saw this tower and the accompanying building far off in the distance from the castle and knew immediately it had to have been designed by famous Hungarian organic architect Imre Makovecz. I've only seen pictures of his work, but it's very distinctive and this simply couldn't have been designed by anybody else. We drove all over Eger trying to find it, and when we did there was a plaque on the wall with his name on it. I was quite proud of myself for having recognized it from so far away ;-).
For more information on Makovecz, go to http://en.wikipedia.org/wiki/Imre_Makovecz and http://www.makovecz.hu/main.html