Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!samsung!think!mintaka!oliveb!amdahl!rtech!llama!glenk
From: glenk@llama.rtech.UUCP (Glen Kilpatrick)
Newsgroups: comp.sys.handhelds
Subject: Mandelbrot on the HP-28S
Keywords: Mandelbrot fractals HP-28S
Message-ID: <4373@rtech.rtech.com>
Date: 28 Dec 89 12:38:04 GMT
Sender: news@rtech.rtech.com
Reply-To: glenk@llama.UUCP (Glen Kilpatrick)
Organization: Relational Technology, Inc. Alameda, CA
Lines: 40


The following plots the Mandelbrot set (invented by IBM fellow
Benoit B. _) on an HP28S.  The required positive integer saved as
BntB is the number of iterations that define a point as being in
the set.  Theory requires _infinity_; I think the _Sci_Amer_ articles
used 1,000.  I suggest 20->100; plots can take HOURS of continuous
computations, and new batteries will probably give you only a few
plots.  Suggested CntrBBM starting coordinates nicely frame the
entire set.  You then INS lower left & upper right corners to the
stack, ATTN, PMIN & PMAX, et al., and restart with _ALPHA_ _NEXT_
BntB Mndlbrt _ENTER_ or _new_param_ _NEXT_ Mndlbrt.  PPAR is
automatically recomputed for the minimal 1:1 rectangle which frames
& centers your PMIN/PMAX inputs.

<< DUP TYPE 0 == << ABS IP 'BntB' STO PPAR 2 GET PPAR 1 GET - C->R
/ 137 32 / / DUP 1 >= << *H >> << INV *W >> IFTE << X PPAR 1 GET
IM PPAR 2 GET IM DUP2 SWAP - 31 / PPAR 4 GET * -> cR ym yM yi <<
ym yM FOR cI cR cI R->C (0,0) 0 -> c z n << DO n 1 + 'n' STO z SQ
c + 'z' STO UNTIL n BntB > z ABS 2 > OR END n BntB > << c PIXEL >>
IFT >> yi STEP >> PPAR 5 GET IM >> STEP CLLCD DRAW { EQ } PURGE {
PMIN PMAX RES CNTR *W *H BntB Mndlbrt } MENU DGTIZ >> IFT >>
'Mndlbrt' STO

<< { (-6.1015625,-1.25) (4.6015625,1.25) X 1 (9,9) } 'PPAR' STO >>
'CntrBBM' STO

*  _ALPHA_ CntrBBM 25 Mndlbrt _ENTER_
*  _INS_ for diagonal corners, _ATTN_, PMIN/PMAX/RES/CNTR/*W/*H
*  _ALPHA_ BntB Mndlbrt _ENTER_ ---or,_e.g.--- 40 Mndlbrt

Question (I don't have the answer for this, but would like to know):
Given that the 28S's mantissa is twelve digits, batteries won't
support a BntB much bigger than 100, and letting CntrBBM be
"one-power", just HOW much magnification is reasonable?  As the
math always computes differences from numbers around _1_, it would
seem reasonable that you can't go lower than 1E12 mag., but my
error analysis isn't that sound....  Feel free to use e-mail, or
even AT&T.
						 Glen Kilpatrick
						 (916)756-9321home