All you have to do is to have all the images of alphabets lowercase and uppercase. Then using some image editor change their orientation by 60 degrees. Design some convention for identifying both lower and uppercase letters and each letter individually.
Once you are ready with that logic of randomly identifying the letter, then you can start with your paint algorithm which will paint the applet with the sequence of words you want.
All you have consider is the co-ordinate system , you have to decide on the start and end point off your applet. Keep on painting the letters with proper x and y values on the applet so that they appear in the way you want.