Using the new random function and simple points plotting, it's easy to create an animated starfield in Basic.

10 PRINT "SHOWING STARS. PRESS ANY KEY TO STOP"                                 
15 DIM X(20): DIM Y(20)                                                         
20 FOR I=0 TO 19                                                                
25 X(I)=RND(I)*512                                                              
26 Y(I)=RND(I)*512                                                              
30 NEXT I                                                                       
35 REM DRAW STARS                                                               
40 CLS $0: CLR                                                                  
42 POINT 0,0,$0,4,1                                                             
45 FOR I=0 TO 19                                                                
50 POINT X(I),Y(I),$FFFFFF,1,0                                                  
51 Y(I)=Y(I)+RND(I)*50                                                          
52 IF Y(I) > 512 THEN Y(I) = 0                                                  
60 NEXT I                                                                       
70 REM SWAP BUFFER                                                              
75 GDSWAP                                                                       
80 GET A$                                                                       
85 IF A$="" THEN GOTO 40                                                        
90 PRINT "DONE"                                                                 
100 END