Many complex patterns in nature such as discharge phenomena are known as fractal objects. With the development of computer system, their spatial structures of discharge patterns have been analyzed using a computer simulation. In this paper, we developed the 3-dimensional numerical simulation model of the electrical tree pattern considering growing probability and local electric field under a Laplace field. Using this numerical simulation model, we obtained the various shapes of electrical tree, such as tree-like, bush-like and densely bush-like (ball-like) trees, and measured the fractal dimensions of these simulated patterns. Furthermore, we studied the relationship between fractal dimensions of 3-dimensional simulated patterns and those of 2-dimensionally projected patterns, and the results were compared with those of the real electrical trees. ƒL •[ ƒ• •[ ƒh:"d ‹C ƒg ƒŠ •[ •A ƒV ƒ~ ƒ… ƒOE •[ ƒV ƒ ‡ ƒ" ƒg ƒŠ •[ •A ƒt ƒ‰ ƒN ƒ^ ƒ‹ •A ƒt ƒ‰ ƒN ƒ 1. ‚Ü ‚¦ ‚ª ‚« Ž© 'R ŠE ‚É ‚Í Ž÷-Ø ‚â ‰Í •ì ‚Ì •ª Šò ‚Ì-l Žq ‚â ƒŠ ƒq ƒe ƒ" ƒx ƒ‹ ƒO •ú "d •} OE`OE`‚È ‚Ç‚Ì ‚ae ‚¤ ‚Ȉê‚Ȉê OE© •¡ ŽG ‚È OE`OE`•ó ‚ª '½ ‚-OE© ‚ç ‚ê ‚é •B ‚± ‚ê ‚ç‚Ì ƒp ƒ^ •[ ƒ" ‚Í •A ‚» ‚̈ê‚Ìˆê •" ‚ð Šg 'å ‚µ ‚Ä ‚Ý ‚Ä ‚àOE³ ‚Ì ƒp ƒ^ •[ ƒ" ‚AE "¯ ‚ ¶ ‚ae ‚¤ ‚È OE`OE`•ó ‚ð ‚µ‚Ä ‚¨‚肨‚è•A ‚¢ ‚í ‚ä ‚é "• OEv "I ‚ȈӂȈÓ-¡ ‚Å ‚Ì Ž© OEÈ 'Š Ž-•« ‚ð-L ‚µ ‚Ä ‚¢ ‚é •B1975"N •AMandelbrot‚Í •A ‚± ‚Ì ‚ae ‚¤ ‚È Ž© OEÈ 'Š Ž-•« ‚ð ‚à ‚Â ƒp ƒ^ •[ ƒ" ‚ð "• ˆê "I ‚Ɉµ‚Ɉµ ‚¤ ŠT "O ‚AE ‚µ ‚Ä •A •uƒt ƒ‰ ƒN ƒ^ ƒ‹ •Afractal•v ‚ð "± "ü ‚µ ‚½(1)•B •ú "d ‚Í •A ‚¢ ‚ë ‚¢ ‚ë ‚È-v ˆö ‚ª 'g ‚Ý • ‡ ‚í ‚³ ‚Á ‚½ •¡ ŽG ‚È OE» •Û ‚Å ‚ ‚é ‚ª •A •ú "d ƒp ƒ^ •[ ƒ" ‚É '…-Ú ‚µ ‚Ä ‚Ý ‚é ‚AE •A ‚» ‚Ì ƒp ƒ^ •[ ƒ" ‚Í ŠK 'w "I ‚È •ª Šò •\ '¢ ‚ð-L ‚µ•A ƒt ƒ‰ ƒN ƒ^ ƒ‹ •« ‚ð-L ‚µ‚Ä ‚¢ ‚é ‚± ‚AE •A ‚¨‚ae‚¨‚ae ‚Ñ ƒt ƒ‰ ƒN ƒ^ ƒ‹ ‚Ì ŠT "O ‚ð-p ‚¢ ‚Ä "ä Šr "I-e ˆÕ ‚É •ú "d ƒp ƒ^ •[ ƒ" ‚Ì ƒV ƒ~ ƒ… ƒOE •[ ƒV ƒ ‡ ƒ" ‚ª ‰Â "\ ‚Å ‚ ‚é ‚± ‚AE •A ‚È ‚Ç ‚ª •Å ‹ß-¾ ‚ç ‚© ‚É ‚³‚ê ‚Â ‚ ‚ ‚é(2)•B ‹C 'Ì •A ‰t 'Ì •A OEÅ 'Ì ‚ð-â ‚í ‚¸•‚¸•A •â ‰• 'Ì ' † ‚ ‚é ‚¢ ‚Í •â ‰• 'Ì ŠE-Ê ‚É • ¶ ‚¸‚邸‚é •ú "d ƒp ƒ^ •[ ƒ" ‚Í •A ŠK 'w "I ‚È •ª Šò •\ '¢ ‚© ‚ç •¬ ‚è-§ ‚ ‚± ‚AE‚ª '½ ‚¢ •B ‚± ‚Ì •ú "d ƒp ƒ^ •[ ƒ" ‚É ‚¨‚¯‚¨‚¯ ‚é •ª Šò •\ '¢ ‚ð ‹L •q ‚· ‚é ‚½ ‚ß ‚É •A ƒR ƒ" ƒs ƒ… •[ ƒ^ ‚É ‚ae ‚é Šm-¦ ƒ‚ ƒf ƒ‹ ‚Ì ƒV ƒ~ ƒ… ƒOE •[ ƒV ƒ ‡ ƒ"‚ª ‚¢ ‚ë ‚¢ ‚ë 'ñ ˆÄ ‚³ ‚ê ‚Ä ‚¢ ‚é •BSawada‚ç ‚Í •A •ú "d ƒp ƒ^ •[ ƒ" ‚Ì •ª Šò •\ '¢ ‚ð •l-¶ ‚µ •A ƒR ƒ" ƒs ƒ… •[ ƒ^ ƒV ƒ~ ƒ… ƒOE •[ ƒV ƒ ‡ ƒ" ‚É ‚ae ‚Á ‚Ä Šm-¦ "I ‚È ƒ‰ ƒ" ƒ_ ƒ€ ƒp ƒ^ •[ ƒ" ‚ð •ì •¬ ‚µ •A ‚» ‚Ì ƒp ƒ^ •[ ƒ" ‚Ì ƒt ƒ‰ ƒN ƒ^ ƒ‹ •« ‚É ‚ ‚¢ ‚Ä ‰ð •Í ‚µ ‚½(3)•B ‚± ‚Ì •ê • ‡ •û Ši Žq ‚AE-• •" ‚ð-p ‚¢ ‚Ä •A2ŽŸ OE³ •ú "d ƒp ƒ^ •[ ƒ" ‚ð ƒV ƒg ‚µ‚Ä ‚¢ ‚é •B ‚» ‚Ì OEã •ANiemeyer‚ç ‚Í •A ŽÀ •Û ‚ÌSF6ƒK ƒ ‚Å "¾ ‚ç ‚ê ‚½ ƒŠ ƒq ƒe ƒ" ƒx ƒ‹ ƒO •} OE`OE`‚ð ƒV ƒ~ ƒF ƒOE •[ ƒg‚· ‚ ‚É •A ƒ‰ ƒv ƒ‰ ƒX •ê ‚Å ‚Ì •¬ '· Šm-¦ ‚ð •l-¶ ‚µ‚½ Šm-¦ ƒ‚ ƒ ‚µ ‚½(4)•B ‚± ‚Ì ƒ‚ ƒf ƒ‹ ‚É ‚ae ‚Á ‚Ä "¾ ‚ç ‚ê ‚½ ƒp ƒ^ •[ ƒ" ‚Í •A ƒt ƒ^ ƒ‹ •« ‚ð-L ‚µ•A ŽÀ •Û ‚Ì ƒŠ ƒq ƒe ƒ" ƒx ƒ‹ ƒO •ú "d •} OE`OE`‚AE ŠK 'w "I ‚È •ª Šò •\ '¢ ‚ð-L ‚µ ‚Ä ‚¢ ‚é ‚± ‚AE ‚ð-¾ ‚ç ‚© ‚É ‚µ ‚½ •ú "d ‚̈ê‚Ìˆê Ží ‚Å ‚ ‚é "d ‹C ƒg ƒŠ •[ ‚à ‚â ‚Í ‚è ƒt ƒ‰ ƒN ƒ^...