Zoom 2/Zoom - Release 2 (1996)(Active Software)[!].iso/graphics/misc/smartfractal/smartfractal.doc

Text File | 1995-01-30 | 49KB | 868 lines

                             Smart Fractal V1.3
                                     by
                              Avogadro Simone

                         V 1.3 release in 30/1/95



                               USER'S MANUAL


 IMPORTANT:  THIS PRODUCT IS SHAREWARE, IF YOU USE AND LIKE IT PLEASE SEND
$10 TO THE AUTHOR. IF YOU DO  NOT KNOW WHAT SHAREWARE IS, PLEASE READ  THE
SHAREWARE.DOC  FILE FIRST, YOU FIND  IT IN THE SAME  ARCHIVE OF THIS FILE.
ALSO  NOTE  'REQTOOLS'   IS  WORK  OF   NICO  FRANCOIS,  REGISTERING   FOR
'SMARTFRACTAL' YOU DON'T REGISTER FOR 'REQTOOLS'.


                                   INDEX

                Chapter 1: The philosophy of the program

       1.1     What's a fractal ?
       1.2     Introduction to Smartfractal
       1.3     What's different (and some background story)
       1.4     Some known spots
       1.5     Other goodies

                     Chapter 2: The program's menu

       2.1     Project
       2.1.1     Informations
       2.1.2     Loading/saving files
       2.1.3     Importing from other programs
       2.1.4     Setting the priority
       2.1.5     Exiting the program

       2.2     Controls
       2.2.1     Graphic controls
       2.2.2     Methods tuning
       2.2.3     Zoom control
       2.2.4     Misc controls
       2.2.5     Buffers

       2.3     Math
       2.3.1     Editing parameters
       2.3.2     Selecting the fractal type
       2.3.3     Determining the type of math
       2.3.4     Regenerating the image

       2.4     Colors
       2.4.1     File operations
       2.4.2     Palette editor
       2.4.3     Choosing the rendering methods !!
       2.4.4     Cycling

                  Chapter 3: Other features

       3.1     Commands of the toolbar
       3.2     Keyboard commands
       3.3     Preferences and setup

                  Chapter 4: Miscellaneous informations

       4.1     How to contact the author
       4.2     Improvements
       4.3     Known bugs
       4.4     History
       4.5     People I wish to thank
       4.6     Bibliography






                Chapter 1: The philosophy of the program

 This chapter contains all the informations needed to use Smartfractal. It
briefly  illustrates the main  features of the  program and gives the user
tips  on  how  to  obtain  some  beautiful  images.  Also gives some basic
informations on what the fractals are.

       1.1     What's a fractal ?

 A  fractal is ... Ehrm... It's a fractal! Just kidding, if you don't know
what a fractal is you will still be able to use Smartfractal but maybe you
will not understand the meaning of some of the options. I won't explain in
depth what a fractal is as this  would require too much space and this  is
not  the  purpose  of  this  documentation.  However there are some simple
things about  fractals anyone  can understand  even without  reading whole
(sometimes  boring) books of  math. First of  all the name: Fractals, what
does this name mean? Basically this refers to the fact that measuring  the
number  of dimensions of one of these 'things' with some modern math techs
(measuring the Hausdorff's dimension)  would give a 'weird'  number (maybe
an  irrational number  or a  fraction, so  'fractal'). This means that the
thing you see on a 2-dimensional sheet of paper has a different  dimension
(Eg.: log(4/3)). Fun, and so? Well, that's difficult to interpret but this
usually  derives from the fact that these  objects are defined by means of
infinite recursion and so you can cut 1/4 of the object and it will occupy
1/3 (!!!)  of the  space of  the original  (that's the  case of the Kock's
curve that you can find on the books used in secondary schools). We talked
about  recursion, together  with infinity  it is  one of  the 'secrets' of
fractals, the beauty of  these object derives from  the fact that you  can
theorically  zoom-in forever  and always  discover new  zones, all of them
will  look  like  the  ones  you  saw  before  but will always be somewhat
different.  The graphical representation  of fractals is  done iterating a
mathematical formula and studying its behaviour for each single point.  As
we cannot afford to examine an infinite number of values for each point on
the screen we usually stop after a finite number of iterations, the higher
the number of steps before stopping, the more precise the drawing will be.
The  fractals you can explore with  Smartfractal are all point-based, this
means that the color  of a single point  depends only on the  behaviour of
that single point. For each point we study the convergence/divergence of a
series defined by the type of fractal and by the point itself, we say that
the  point is in  the set if  the series converges,  otherwise we say that
it's out of the set. The deeper we go into the set and the harder will  be
to  determine if a point generates a series that diverges or converges and
so  the  higher  will  be  the  number  of  iterations needed to obtain an
acceptable image of that zone.

       1.2     Introduction to Smartfractal

 The  very first time  you will run  Smartfractal (Smart from  now on) you
will probably want  to setup the  preferences as the  default behaviour of
Smart  is to use parameters acceptable on  the most basic machine (like my
A500 :-),  just browse  the control  menu to  set the  desidered number of
colors, the correct image size and the most suitable number of iterations,
if  you don't know  what this means  then you'd better  read the whole 1st
chapter before beginning for better results. Now go to the colors menu and
set the internal and the external coloring methods (these are peculiar  to
Smart!),  now choose the fractal type  you prefer and save the preferences
in the 'S:' directory, call them 'SmartFractal.prefs'. Done? O.K. You just
finished  the  basic  setup!  From  now  on  Smart  will  start  with your
preferences. Maybe you now want to zoom in, if so just click in the center
of  the zone you want to zoom, adjust the box size with the gadgets on the
right side and click on the zoom gadget (or select the zoom option in  the
control  menu), Smart will  start to calculate  that area. After a certain
number of  zooms you  will probably  decide to  zoom out,  just select the
unzoom  menu!  If  you  cannot  find  anything beautiful you may decide to
render pre-determined zones, if so just read paragraph 4!

       1.3     What's different (and some background story)

 What you have been  doing up to now  was possible even in  the most basic
fractal  generator, so what  does Smart do  that others don't?  I chose to
write Smart after re-reading a  book talking about fractals, the  pictures
on that book looked somewhat nicer than the ones I could generate with the
available  programs. The main difference was that these pictures were also
colored  internally,  this  gave  them  a  totally  different  look. I was
disappointed not to have a program to do that, unfortunately the tech used
to  color that  pictures was  really time  consuming and would have slowed
down  the  generation  of  images  to  an  unacceptable rate even on 68040
machines,  so I gave off for some  time. Sometime later I happened to look
again at that book and noticed that  some figures used a tech to draw  the
external  part that was  quite simple to  implement but still  I could not
find any program able to do that, what a shame, I thought, but then I  had
an  idea: Why not to  create my own rendering  tech for the internal zones
and use  the one  seen in  the book  for the  external ones  ? I  began to
program  and in less than  a week I discovered  that my techs worked quite
good, I just had to  write everything except from the  rendering routines,
but  I were so  happy that the  things went on  by themselves. Some months
after (I  had some  exams to  do so  I left  the project  for some time) I
stumbled  into a disk with the word "Smartfractal" written on it, I picked
it up, created the  user interface, added many  features and after a  hard
work  I came up with  the very first beta  version. Some month have passed
from that day and with the new versions I have added anything I could find
useful to the program.  The program you are  using now is the  result of a
hard  work and  so I  would appreciate  any form  of encouragement as I am
human too  :-). Just  write a  postcard if  you really  do not think to be
worth supporting me ;-( that postcard will let me know that there's people
out there that appreciates my work !


       1.4     Some known spots

 If  you ever happened  to read a  book about fractals  surely you'll have
desired to render the same  pictures, apart from the problem  mentioned in
the  previous paragraph,  sometimes the  informations on  how to  get that
pictures are omitted! So I  decided to include a directory  containing the
preference  files needed  to render  some very  known images and some less
known ones that  I think to  be worth a  look! If you  want to render such
zones  just  select  'Prefs->Load  spot'  and  than  look into the 'Spots'
directory in the same directory of Smart. You'll notice that the spots are
divided according to the type of  fractal. If you want to render  an image
never  seen on books just enter the 'Volterra' dir and load the 'Seahorse'
spot! Other unknown spots are found  in the dirs of the inverted  sets (by
now  Julia, Mandelbrot and Julia parameter  plane), you can also find some
beautyful spots in the 'Weird' directory, these are funny images  obtained
by setting 'not too meaningful' parameters, most of them can be considered
interference  images, because  of this  most of  the spots  in the 'Weird'
drawer should be loaded as preferences.

       1.5     Other goodies

 On suggestion I added two new directories: 'Colors' and 'Prefs', they  do
contain  some pre-defined colors for both AGA and non-AGA machines and the
basic preferences for the different types of fractals.


                     Chapter 2: The program's menu

 This chapter explains the meaning and the use of the various voices found
in the menus.

       2.1     Project

 This menu contains all the controls concerning general operations.

       2.1.1     Informations

 There are two voices giving informations  in this menu. The first one  is
"info",  it gives  informations on  the type  of fractal that is currently
set, the window being drawn, the number of colors, iterations and the type
of math that had been used to render the current image (useful in case you
are using  the "auto"  mode), it  also states  if the  selected fractal is
parametric  and if it's  parametric it shows  the value of the parameters,
also present the configuration found by Smart (CPU+FPU+AGA support),  also
if  you turned  buffers on  you'll find  here the  amount of  mem taken by
buffers. The second voice giving  informations is "about", this shows  the
program  name, version  and revision,  a shareware  message and my contact
address.

       2.1.2     Loading/saving files

 With  the  "project"  menu  you  can  either  save  the current situation
(comprehending  all  of  the  preferences)  together  with the image being
displayed, or  save only  the current  settings (comprehending  the window
position, fractal type, math, colors etc.). If you want to save everything
(ie.:  Image+settings) choose the "save" option directly in the main menu,
the situation will be saved as a standard iff image followed by a  special
field added by Smart to be able to recall the infos about that image. Once
you  want to recall that situation just select "load" in the main menu and
the  situation  will  be  restored.  If  you  want  to  save/load just the
situation  but  not  the  image  choose  the voice "prefs" and than select
"load" or "save".  Note that you  CANNOT recall only  the situation (saved
with  the "prefs" voice)  using the "load"  in the main  menu, this is the
case of the spots  present in this package,  you must use the  "load spot"
option from the "prefs" voice. Before saving the whole image you can go to
the options an turn iff compression on/off, note that if you are saving to
an  autocompressing device you'd  better leave it  off as the standard iff
compression method is run-length 1, that's quite inefficient. Please  note
that if you load an image saved with Smart in an art package and than save
it  back the package will NOT retain  the information about the fractal so
you won't be able to reload it with Smart, so when you do retouch an image
do not save it over the original  or you'll not be able to reload  it with
Smart!

       2.1.3     Importing from other programs

 From  V1.3 Smart offers you the option to import from other programs your
favourite  spots,  just  select  "Prefs->Import"  and  pick the data file,
actualy  Smart  supports  the  following  formats:  Mandelmania,  MisterM,
Lyapunovia, MandelA (this is now 100% as I had to guess the format :-), if
you use a program  other than these you  may try anyway to  import as many
programs  do use Mandelmania-like  data files. If  this fails and you have
want me to add an other format simply write to me.

       2.1.4     Setting the priority

 The  project  menu  has  a  "Priority"  voice, it will pop-up a requester
asking  a number in range -10..+10, this will be the Smart's priority. The
higher the number, the  higher the priority. If  you want to do  something
else  while drawing fractals  you'd better set  this to -1,  this way most
programs will have higher priority  and will give prompt response  to your
imputs.  In some cases it may be useful to set it to lower values but this
should be rare. You  may use positive values  to speed up a  bit, but this
will be a realy little bit. Be aware that setting a priority higher than 5
may  cause  some  you  some  problems  as  all  standard  programs will be
unresponsive while Smart will be calculating (and with fractals this might
take a lot!).

       2.1.5     Exiting the program

 This  is  the  simplest  thing,  just  select  "Quit"  and you will see a
requester  come up to ask you if you  really want to exit, just select yes
and you  will terminate  Smart. If you  are using an  Unregistered version
of  Smart a requester will pop-up asking  you to register (sorry, it's the
rule :-).

       2.2     Controls

 This  menu contains all  the controls concerning  the aspect of the image
and giving controls about the zoom method and options.

       2.2.1     Graphic controls

 There are  four voices  controlling the  appearance of  the image  on the
screen.  The first one is "Size", this enables  you to set the size of the
image to render, there  are 4 predefined sizes  and a "custom" option.  If
you  chose the "custom"  option you'll get  a requester, if  you are using
Kickstart V2.0+ you'll  get a ScreenMode  requester and you'll  be able to
select any available resolution (comprehending any non-standard resolution
available via third-party Monitor Types) and number of colors, please note
that  you's  better  NOT  select  special  modes or non-proportional modes
unless  you  want  to  make  some  weird tests (non-proportional modes are
1280x512  and  640x256),  so  if  you  wand  to  create a backdrop for the
Workbench you  should select  Laced-Hi Res  and than  convert the image to
non-laced hi res with a graphic package (Dpaint will do). If you are using
KS1.3  or less you'll get  a string requester and  you'll be able to enter
the desidered vertical size, the horizontal one will be determined by  the
"aspect" option, if you choose a vertical size lesser then or equal to 256
the  screen size will be  320x256 and your selection  will affect only the
size of the image. If you choose a number greater than 256 you'll also set
the size of the  screen, remember that the  screen will always have  a 5/4
aspect (that's the default on PAL machines), if you choose a vertical size
greater  or equal to 400 you'll get a hi-res interlaced screen. The second
voice influencing the image is "aspect", you can select either "square" or
"rectangular" to set the aspect to  4:4 or to 5:4 (like the  screen). Than
there is the "colors" option, you can there choose the number of colors on
the  screen, please note that  Smart will try to  open the screen with the
desidered number of colors even if your machine has not the capability  to
display  them, this will blank the screen  if you select 64 colors (that's
extra half bright)  or more and  hi-res on a  non AGA machine  with KS1.3,
this  causes you not  to be able  to see anything  on the screen, the only
solution is to  terminate the drawing  pressing Amiga-X and  after a while
pressing  return,  then  press  Amiga-Q  and  finally  'Y'  to quit Smart.
Surprisingly selecting 256 colors on KS1.3 in low-res will result in  just
32  being displayed but 8 being stored in memory, so you can draw and than
store 256 color images that you'll  be able to display on AGA  machines or
with  video enanchers.  Please note  that some  resolutions will slow down
significantly the drawing on non-AGA  machine, that's not a bug,  it's due
to the internal multiprocessing architecture of the amiga that assigns too
few  time to the 680x0 (ie.: that's the  case of 16 color hi-res where the
machine almost stops). Then there is the "title" toggle, with this one you
can turn on/off the  screen title (if you  turned it off, selected  a full
screen  image and turned on autozoom then  use Amiga-N and Amiga-M to move
the screen to front/back without zooming).

       2.2.2     Methods tuning

 In this menu you can set two options to control the methods to render the
image,  both  of  them  will  give  you  control  on  the  accuracy of the
representation.  The first one is "Depth",  with this voice you can select
how  many  iterations  to  take  before  deciding that a point generates a
series  that  converges.  Keep  this  number  high to have a more accurate
representation of the image, keep it low to have a fast one, note that the
deeper you go into the image the higher will have to be this number to get
a realistic representation. If you have yet completed the image and  raise
the  number of iterations  a requester will  pop-up asking if  you want to
update instead of redrawing, if the internal color is solid and the Buffer
is on will be able to  choose either "Fast" or "Exact", unless  the number
of  iterations is  too high  you'd better  select "Exact", if the internal
color is  not solid  but the  buffer is  on you'll  be able to select only
"Exact"  or  no  update.  The  second  voice  concerning representation is
"Blocks", it allows you to set how big the blocks will be and so how  many
passes  will the image take  to complete, from V1.3  of Smart you may also
select "Tesselate". If you turn tesselation on the screen will be  divided
in  two blocks, each block will be  divided into two smaller blocks and so
on, this may introduce a BIG error in some cases and may be error-free  in
others, the problem is that with this mode an area surrounded by pixels of
the  same color is considered to be  filled with that color, this would be
true if pixels had no size, but may cause approximation in real life.  You
may also select to use the 'traditional' blocks, this gives you control on
the  degree of approximation in drawing  the image, the bigger the blocks,
the faster will be  the rendering and the  more you are like  to lose some
details.  This option should be used with  care as it has a big potential,
there  are  zones  where  setting  the  blocks  to 8x8 will not affect the
quality  of the image but will speed up its generation more than 10 times,
in  other  zones  even  setting  the  2x2  option  will  give  you a quite
inaccurate  representation  of  the  image  and  will not be significantly
faster than the pixel-perfect 1x1 mode.  There is no way to tell  what the
best  block size  is, generally  4x4 should  not affect  significantly the
image integrity but will  give a great speed  improvement. If you use  the
8x8  option be careful to set a  higher number of iterations to compensate
the possible imprecisions.

       2.2.3     Zoom control

 There are four voices concerning zooming  in this menu. The first one  is
"zoomrate",  it allows you to set how much you will zoom, that is how much
of the zone around the point  you selected will be zoomed. The  second one
is  "autozoom", just select "on" or "off". If you turn it on each time you
want to zoom you'll just have to click in the center of the zone you  wish
to  zoom and the  zoom will take  automatically place even  if you did not
select  the  voice  "zoom".  The  voice  "zoom"  is used when the autozoom
feature is off to zoom in a zone, just select this voice and than click in
the  center of the  zone you want  to see, if  you want to cancel the zoom
just click outside of the image or press the right mouse button. The  last
option  "unzoom" lets you zoom  off the current image,  just select it and
the image will be recalculated automatically without further actions.

       2.2.4     Misc controls

 There are four more toggles providing generic controls on the setup. This
toggles are "Autoredraw", "Pack iff", "Be quiet" and "Toolbar", the  first
one  let's you  disable the  auto-update function  that redraws  the image
after any change in the settings, when this is off the redraw will  happen
only  if the screen had been rebuilt and the image disappeared. The second
toggle is to turn on/off the  iff compression (see above for more  infos).
When  the "Be quiet" switch is on you won't be prompted before overwriting
existing files and you won't be presented a requester once the drawing had
terminated (this will also turn off the screen-to-front feature). The last
toggle  is  "Toolbox"  and  when  activated  (by default) will turn on the
toolbar.

       2.2.5     Buffers

 The  last option in this menu is "Buffers",  you may turn it off or on as
all toggles. When you turn it on you'll get a requester asking if you want
full buffering or 3DOnly buffering. If you select "3DOnly" you'll be  able
to  see the 3D Overlay once the  drawing has been completed, and will also
be able to use the Update functions (more iterations of different type  of
coloring),  turning  on  "3DOnly"  will  not  slow  down significantly the
calculations (about 0.5-2 secs). If you select a "Full" buffer, you'll get
by default the 3D Buffer but you'll also get the color buffer, when it  is
active  you may change  the internal/external coloring  method and get the
screen updated immediately, this will unfortunately slow down the  drawing
a lot, from 2 to 40 secs !!!. If you know in advance that the drawing will
take  a big amount of  time and have enough  memory you'd better turn full
buffer on, else, if you are  just browsing, you'd better turn on  only the
3DBuffer.  Please  note  that  the  buffers  are  allocated when you start
drawing so don't  worry if the  info window says  that there's no  buffer,
also  note that turning the  buffers off will also  free the allocated mem
immediately.

       2.3     Math

 This  menu  contains  all  the  voices  that  involve  direct  control of
mathematical aspects of the drawing.

       2.3.1     Editing parameters

 As  Smart  features  parametric  fractals  (Julia,  Volterra-Lotka, Julia
Parameter plane  and Lyapunov  space) it  also enables  you to specify the
value   of  these  parameters.  Julia,  JuliaPP  and  Volterra  do  use  2
parameters,  in  the  Julia  sets  the  parameter  is a complex number and
indicates  a point of the corresponding Mandelbrot set, if while examining
the Mandelbrot set you wish to  pick a point and set the  Julia parameters
to  that  point  just  select  the  "set  point"  voice  and  click in the
Mandelbrot set on the point you  wish to use (Tip: just after  setting the
point  switch to the Julia set, you'll get a view of the same window as it
appears in the Julia set and it will look similar to the region you picked
the  point  from,  the  nearer  to  the  point  you'll  go  the lesser the
differences  will be :-). However you may know some values (maybe you have
a  book)  and  want  to  introduce  them  manually,  if so just choose the
"edit point" option and you'll get a requester asking for the real part of
the parameter and then for the imaginary one. If you changed your mind and
no longer want to edit the parameters just hit return twice. Maybe you got
also the coordinates of the window you have to zoom, if so just choose the
"edit window"  voice and enter the value you wish to use (once again press
return to keep the actual values). Note that the window requester will not
allow you to specify all the four values as you may have expected, this is
because Smart does not want you  to get weird image aspect (after  all who
wants  a  Mandelbrot  set  that  looks  deformed ??). A different approach
should be used for Lyapunov space,  here you may set the sequence  and the
color  divide. The color divide  is a number that  says how much shoul the
palette be spreden around,  the higher, the lesser  you'll be like to  see
the  same  color  used  twice,  the  lower,  the  more  you'll  be able to
distinguish potential of points. To set the color divide just select "edit
point", you'll be prompted a number (by default the old value). The second
parameter is the sequence to be used generating Lyapunov space, this is  a
sequence of 'A' and 'B' (no matter the case), each letter in this sequence
has the following meaning : 'A' means that the 'x' value should be used in
the  iteration, 'B'  means that  the 'y'  value should  be used. So if you
select 'ABB' the first iteration will use 'x' as parameter, the second and
third will use 'y' and than the sequence will repeat (the fourth will  use
'x',  the fifth and  sixth will use  'y' etc...). So  don't use a sequence
with more letters than  the iterations as this  has no meaning, also  note
that  even if the number of iterations should be big to let the succession
converge you may leave it low to get nice pictures (this is what's done in
Lyapunovia), after all you want to create nice pictures, if you wanted  to
examine population dynamics you'd have used something less fun !
 If  you want to make a  3DOverlay or have made it  yet and want to change
it's appearance  you may  "Set 3D  Opts", you'll  be asked  level % of the
plateou  and the reduction, the first means how many iterations will be in
the graduated  part (if  you set  50% and  have 719  iterations the points
exiting  with 0-359 iterations  will hav different  heights and the points
with 360-719 iterations will be part of the plateou). The reduction  level
is  used to adjust  the height of  the 3DOverlay, by  default if will be :
height=(maxiterations * (level%))/Reduction.


       2.3.2     Selecting the fractal type

 This is  easily done  by selecting  the "set  fractal" voice  and then by
choosing  the fractal you  prefer. Mandelbrot and  Julia are the classical
ones  found  in  almost  any  fractal generator, Volterra-Lotka is fractal
taken  from  the  book  I  have  (see bibliography for more informations),
Inverted Mandelbrot and Inverted Julia  are the Mandelbrot and Julia  sets
projected  into an inverted space (again see bibliography). Than there are
Julia Parameters plane and Inverted Julia Parameters Plane, Mandelbrot  is
the  Julia Parameters Plane of the origin  of the Gauss plane (0+0i), here
you  may  choose  to  generate  Parameter  Planes of other points. Finally
there's  Lyapunov Space, this one is like  the one found in Lyapunovia and
is basicaly the logistic equation  for a single population drawn  changing
the  maximum population between  an iteration and  the other (see previous
paragraph). When you set  the fractal type you  may want either to  redraw
(Mandelbrot->Julia->JuliaPP) or to restart (Mandelbrot->Volterra->Lyapunov
etc...), a requester will pop-up, just selcet what you prefer.

       2.3.3     Determining the type of math

 While  exploring fractals one of the most important problems is to choose
a precision that enables to draw an image that is free of defects, but  at
the  same time it's important not to  exaggerate not to slow down too much
the calculation (I won't tell how long does a double precision image  take
to  render in  640x512 on  an A500  but know  that I  care too much for my
computer  to  risk  leaving  it  on  the  whole  night).  So you'll surely
comprehend  that the more precisions are  available the better it is. Some
programs (ehrm...  Actually I  know only  of Mand2000  that's a commercial
program!)  do offer  special routines  to handle  almost any precision but
you'll usually find that even on  fast machines (68040 33Mhz I mean!)  any
precision  higher than  the extended  FPU precision  will result quite too
slow to  use in  non-background situations.  Smart offers  you 6 different
precisions,  they are  (in order  from the  fastest to  the most precise):
Turbo integer, integer, big integer, floating point, double precision  and
extended  FPU precision.  The first  five are  available to  anyone on any
machine, the sixth one  is only available to  FPU owners and 68040  owners
with  fpu-patches (see below).  Smart offers you  to do the selection work
for you,  just choose  the "auto"  option and  you'll never  have to worry
about  the type of math  used (Tip: when drawing  the starting image of an
inverted  Julia  force  the  precision  to  integer, the zones near to the
borders  will be pixelized but the effect may  be fine (I like it!) and it
will also be faster (unless you have an FPU!), Smart had been designed  to
be  as precise as reasonable so I did not set that tip into the program as
default). Please note that if you are  drawing a zone on the border of  an
inverted  Julia that is quite big (the  set not the region!) Smart may get
confused and select the wrong precision, you'll notice it as you'll get  a
pixelization  effect! In these cases you can  use the other options of the
"precision" voice to  force Smart to  use a specific  precision, note that
you  cannot force the Turbo integer precision  as it's useful only on some
occasions and Smart will activate it automatically while using the  'auto'
mode,  also note that  if you don't  have an FPU  and try to force the FPU
routines Smart will complain, if you decide to go ahead anyway expect your
machine to crash as I wrote  the FPU routines in assembler using  directly
the  coprocessor istructions and  not the library  calls that are too slow
(but useful  if you  need to  write a  single source  that uses either the
emulation  routines either the FPU,  in this case I  wrote a separate code
for  processor-based  calculation  and   so  there's  no  reason   to  use
libraries).  Tech note  on how  Smart decides  the precision to use: While
developing Smart I assumed that anyone owning an FPU also owns a processor
that will  compute faster  in integer  (and turbo  integer!) than  the FPU
(that's true if you have a 68020 or more, if you have a FPU and a 68010 or
less  always force the precision to FPU, by the way: why did you do such a
strange thing as connecting a 32 bit FPU to a 16 bit bus ?). Note to 68040
owners: Before  using Smart  you must  run a  system patcher  to trap  the
line-f  exceptions generated by the FPU istructions not supported by 68040
internal FPU, once done this (you probably yet installed it in the startup
:-) you can safely run Smart  and enjoy your machine's FPU speed!,  if you
don't install the patch you'll still be able to use Smart but you won't be
able to use FPU mode.

       2.3.4     Regenerating the image

 There  are two options to regenerate the image, the first one is "redraw"
and will redraw exactly the selected window with the selected  parameters,
this  is  useful  when  after  changing  the  coloring methods you want to
regenerate the image with the new routines. The second option is "restart"
and as  you'll have  guessed selects  the default  starting window for the
selected  type of set before redrawing. If  the 3DBuffer is active but you
closed the 3DOverlay window and want it back, just edit 3DParametes,  keep
them as they are and you'll get the 3DOverlay back.

       2.4     Colors

 As  beauty is a subjective idea people  may wish to change the appearance
of the fractals on the screen, this menu does this but it also allows  you
to select the coloring methods of internal and of the external part of the
various  sets.  Note  that  this  is  not  just  an exterior change as the
different  methods  give  different  informations  on the behaviour of the
single points.

       2.4.1     File operations

 The  two voices "save"  and "load" allow  you to save  and load the whole
color palette used by the program  (all 256 colors) in iff format  so that
you'll  be able to use palettes  edited in your favourite drawing package.

       2.4.2     Palette editor

 Just  choose "edit" from the  menu and you'll be  faced with the standard
color requester of the ReqTools library, freely edit the palette and  than
choose 'ok' or 'cancel' to confirm the changes or to discard them.

       2.4.3     Choosing the rendering methods !!

 As I wrote before, this is the main difference with all the other fractal
generators  I could find on Amiga, Smart can assign a color also to points
internal to the set  !. There are two  menus concerning this options,  the
first  one is "external" that  allows you to specify  the type of coloring
you want  in the  external regions.  Here you  have six  choices: "Solid",
"Smooth",  "Binary", "2Binary",  "Checked1" and  "Checked2". The first one
will assign to all  the points not in  the set the same  color. The second
one will assign the usual coloring that's based on the speed of divergence
(this evidences the level curves). The third one is the one I talked about
in chapter one, this is a simple method that assigns to each point outside
the  set a color depending on where the point was when it exited the limit
circle of  divergence, the  color depends  on the  argument of the complex
number,  this brings in evidence the  Hubbard's angles of various point of
the Mandelbrot and Julia sets.  The fourth method is a  personal variation
of  the  third  that's  based  on  a  different  assignment  of the colors
depending an the argument. The fifth and sixth are obtained by mixing  the
"Smooth"  and  "Binary"  options,  they  are  very  impressive  if cycled,
otherwise  they  look  almost  like  "Smooth". The second voice concerning
coloring (and the most important in my opinion :-) is "internal" that lets
you  specify  five  types  of  coloring, they are: "Solid", "Logarithmic",
"Smooth type 1", "Smooth type 2"  and "Logarithmic type 2". The first  one
works as the corresponding one in the external menu, the second, third and
fourth  one give you an idea of how much difference there is in the module
of point end of its (probable) attractor, the fifth one gives you an  idea
of how far the point is from its attractor. The second and the fifth adopt
a  logarithmic  scale  so  to  allow  you  to  see with the same precision
attractors of different orders, the third and fourth do adopt a  corrected
proportional  method, that's less efficient than the logarithmic scale but
it's more colorful and in some cases gives you more informations. The most
significant method in terms of math is the fifth one that does its  better
to  evidence the internal level curves (that's  how fast a point gets near
to its attractor), this is the most similar to the one I found on the book
I wrote about in the previous chapter,  I cannot be sure if it's the  same
but  I believe it to be, the real  problem is the nature of the attractors
that  present  a  periodical  nature,  to  evidence  the biggest number of
attractors  the number of iterations should  be equal to ((K!)-1) that's a
number too high even with K=10 (K=10 -> depth should be = 3628799, too big
for me!). This is a common problem with all the internal coloring methods,
if you use it just select at  least an odd number (that's due to  the fact
that  on some fractals, like Mandelbrot,  the main attractor (that's 0+i0,
the origin of  Gauss' plane) is  present in all  the periodical orbits  so
that  if you choose an even  number all the point will  look to be part of
the domain of the origin!.

       2.4.4     Cycling

 From V1.1 Smart offers the cycling option, you can use the voices of  the
"Cycle"  item to  turn on/off  cycling, select  the direction  of cycleing
(forward or  backward) and  to speed  up or  slow down  the cycling of the
colors.  You can change the direction of cycling while it's on without any
problem. If you stop  the cycling the colors  will remain the ones  of the
moment  you stopped  it, if  you want  to revert  to the  original palette
select the "Reset" option, if you want to let the actual palette be  fixed
just select "Edit" and click on "Ok" without modifying anything.


                  Chapter 3: Other features

       3.1     Commands of the toolbar

 From  V1.2 on Smart features a toolbar that holds buttons for some of the
most used  commands, it  also offers  a couple  of functions NOT available
from  the menu. The top two gadgets are used to increase/decrease the size
of the zoombox (and so to control the zoomrate), the two just below  allow
to  zoom/unzoom and  the first  of the  next line  let's the user hide the
zoombox (not available from menu). The one immediately on the right  let's
the  user turn  on/off the  coordinate disply  option, when this option is
active  if  the  cursor  passes  on  the  image  the  coordinates  of  the
underlaying point will be displayed, this is really useful while using the
"Set  point" option. The four  buttons below these ones  allow the user to
turn on/off the color cycling, change its direction, speed up or slow down
it. There are  than two icons  to show the  information box and  the about
message. The last two buttons will let the user save/load everything.

       3.2     Keyboard commands

 Many  menu options do  have a keyboard  shortcut, and can  so be used via
keyboard, however there is a simply trick available only from keyboard, if
autozoom is off and the zoombox is  visible you can use the arrow keys  to
move it around the image.


       3.3     Preferences and setup

 If  you want Smart  to start with  your configuration as  default you may
save your  preferences as  "SmartFractal.prefs" either  the "S:" directory
either  in the same directory of Smart,  note: if you run Smart from SHELL
you'll have to save the  preferences in the 'current' directory,  I.E.: if
you  are  in  directory  "HD1:Utils/"  and  Smart  is  in  directory "HD2:
Utils/Math/SmartFractal" (and it is the path) you can run Smart by  typing
"SmartFractal",  but  if  your  preferences  are not in "HD1:Utils/" Smart
won't use them.  So if you  frequently use Smart  from SHELL you'd  better
place  the preferences in  the "S:" directory.  An other feature that will
surely be appreciated by  someone is that you  can use any image  obtained
with  Smart as default one, just save it as "SmartFractal.iff" in the same
directory of Smart (the notes for SHELL  users about preferences are still
valid).
 Another feature that SHELL users will appreciate is that from V1.1  Smart
will  auto-detach  from  the  current  process,  running in background and
letting  you  close  the  Shell  whenever  you want without having to quit
Smart.


                  Chapter 4: Miscellaneous informations

       4.1     How to contact the author

 Well, if you have been reading the document you'll probably have also the
program and my contact address but anyway here it is:

 Mail to:      Simone Avogadro
               viale Rimembranze, 33
               Appiano Gentile
                 22070 (CO)
                  ITALY

 E-mail on Internet to: [e-mail]

 If  you cannot access the internet but have access to the Fidonet you can
use a  gateway to  Internet, if  you don't  know how  to do  that ask your
sysop,  as I don't have direct access to  Fidonet I cannot tell you how to
do it (sorry:-),  but note that  this method is  slow (usually it  takes a
month or more for the mail to arrive to me!).
 There  are no known bugs in Smart but  I can't tell if there are not bugs
or if  we simply  don't now  about them  :-}, if  you find  any bug please
report  it to me, possibly with a  clear description of how to recreate it
(please state the  machine configuration you  have, etc.). Reporting  bugs
helps me to keep the program safe so, expecially if you found a nasty one,
report it to me as soon as possible.

       4.2     Improvements

 Here  I give a  list of improvements  that I'd like  to add to Smart if I
have time (Ie: If I successfully take my exams) and if I feel Smart to  be
appreciated (feedback is important, even an E-mail makes the difference!):

 o Make use of MUI library for 2.0 users
 o Support for xpklibrary de/compression
 o A "Pickup" menu so that you can stop drawing, save the partial work
   and than pickup your work later (very useful for time-consuming
   drawings!)
 o A speedup buffer, so you can zoom faster
 o Faster rendering routines
 o Better color cycling feature
 o 3D mapping of fractals (spherical and continuous axonometrical)
 o More types of fractals
 o More coloring techs

 Changes that will take a bit more to be done:

 o Arexx support (I got the documentation for it and I will do it as
   soon as I have enough time)
 o Real-time zoom (like Mand2000)

 As you see I have a lot of ideas and so there are a lot of possibilities,
let  me know  your preferences  and if  you have  any proposal for special
features not mentioned here (please don't just say: "I want Smart to  draw
in  real time, support  custom fractals and  display images directly on my
Virtual reality glasses" :-).

       4.3     Known bugs

 There's only a known bag so far,  if you use KS1.3 you may happen  to see
timings like 0:00:00. I'm sorry for this, under KS1.3 the timing functions
of  the OS  are quite  inaccurate and  I didn't  want to  write own timing
functions (lazy guy :-).
 There's another problem, some  precisions may contrast with  some drawing
options,  so far Volterra and Lyapunov  won't work with BigInteger math so
Smart overrides these modes and switches to Float. If you use  Tesselation
you  won't be able  to use Float  as Smart will  override your options and
switch to  Double, this  should not  be a  problem as  the use of Float is
quite  restricted,  infact  the  difference  between BigInteger a Float is
little, so probably you'd have to switch to Double quite soon (a couple of
zooms).
 This final  one is  not a  bug but  rather an  advice. From V1.2 the info
window also displays infos on the machine it detects, CPU+FPU are OK but I
don't  know a SAFE way  for identifying AGA and  so it detects KS3.0+ (AGA
support) and not the chipset.

       4.4     History

 V1.0 in 14/6/94 : First release
 V1.1 in 18/7/94 (Internal) : Never released but really stable.
   - When run from CLI/SHELL it now auto detaches and goes in background
   - Added two voices to Prefs menu to load separately Options and Spots
   - Added the option to compress images with standard Iff method
   - Added color cycling
   - Added "Be Quiet" toggle
   - Added the zoombox
 V1.2 in 20/9/94 : No known bugs.
   - Added support for any system monitor with a standard Screenmode
     requester
   - Added a toolbar to make interaction more immediate and intuitive :->
   - Added new fractals "JuliaPP" and "Inverted JuliaPP"
   - Added 64 bit integer math, about 3-4 times faster than "float" and
     90% of the times with equivalent precision, made separate versions
     for 68000-010 and 68020+
   - Added the ability to show cursor coordinates on the screen title
   - Fixed a bug in V1.1 that caused some problems with packed iff
   - Now Smart asks for confirmation before overwriting existing files
     this feature can be disabled with the "Be Quiet" switch
   - Fixed a bug that didn't allow to use more than 65535 iterations with
     FPU precision
   - Micro-buffering almost halves the time taken to render quite uniform
     areas.
 V1.3 in 20/1/95 : No known bugs.
   - Added the option to import alien preferences, support for:
       Mandelmania, MisterM, Lyapunovia, MandelA (not 100%).
   - Rewrote some FPU stuff, now 5-10 % faster!
   - Added a new set type: Lyapunov Space
   - Added 3D buffer, allowing 3D overlay (quite primitive but still
     better than nothing :-)
   - Added Color buffer, lets you change the coloring method without
     having to redraw (when active about 2-40 secs slower :-< ).
   - Added "Auto update", if you raise the number of iterations you'll
     be able to redraw only a minor part (Idea from Mand2000 :-)
   - Added a new drawing mode: Tesselate (Like MisterM, FractInt an
     others), about 20-40% faster !
   - New 3.0 Look even for KS1.3 owners!
   - Finally fixed the 24Bit color support, now you can use 24 Bit colors
     in all of their glory!
   - Fixed problem with Autoscroll (not active in V1.2!).
   - Added AmigaGuide documentation.
   - Added some new spots.
   - Added a timig feature, now you know exactly how long it took to
     complete the image
   - Added option to set program priority


       4.5     People I wish to thank

 Oh, well, there's  a lot of  people I should  thank, so in  no particular
order:  Mom, dad and  my brother for  supporting me and  being patient, my
friends for their interest and then in particular:
 Stefano Volponi for  correcting the errors  in this text  (as you'll have
supposed English is not my native language!)
 Donato  Corvi for beta-testing  on his fat  A1200+68030 33Mhz+68882 48Mhz
FPU +8Meg 32Bit fast. Also for letting  me work at his home in an  attempt
to  fix a nasty bug  with FPU (finally I  caught it!). Most of the awesome
new spots found in V1.2 are due to his research.
 Cristiano Preda for beta-testing  on his monster (A2000+8Meg  32bit fast,
68040  30Mhz, 2Meg Merlin  graphic adapter), and  for procuring me the iff
documentation.
 Other people I wish to thank:
 Fabrizio Sala (sysop of Fast Enough BBS) for spreading (I hope!) Smart on
Fidonet
 Nico François for  developing the ReqTools  library (req.library is  cool
but reqtools is cooler!) (if you want to know more about Reqtools read the
SHAREWARE.DOC file)
 Enrico M. Ferrari for paying attention to SmartFractal and for his review
on MC MicroComputer
 And all the others I forgot!

       4.6     Bibliography

 The book I wrote about many times in this text is:
H.O.Peitgen  -  P.H.Richter,"The  Beauty  of  Fractals,  Images of Complex
Dynamical Systems",1986, Springer Verlang - Berlin, Heidelberg, New York.
 If you have a secondary school  preparation and like math you'll be  able
to  comprehend the principles explained in this book and even if you don't
understand mathematics you'll find  the Interventions very interesting  as
they  are comprehensible  by anyone  and express interesting philosophical
considerations; you'll also find an  interesting appendix on how to  write
simple  programs  to  generate  fractals,  if  you are a bit more advanced
there's  a  section  commenting  some  advanced  techs  you'll surely find
interesting (even if some do require too much computational power to adapt
them  for our amigas). If you are Italian  (As I am!) you'll also find the
Italian translation of this book,  it's called "La Bellezza dei  Frattali"
and  is  published  by  Bollati-Boringhieri,  I  found  it  to  be  a good
translation not presenting problems with traslation of mathematical therms
(thanks to the work of Umberto Sampietri).
 If you want to read something more practically-oriented you should try to
procure  old  numbers  of  "Scientific  American"  (or  translations) that
featured   interesting  articles  about   fractals  and  non-deterministic
dynamics.
 If,  instead,  you  are  more  interested  in the mathematical aspect you
should  search for a book of  B.Mandelbrot that's considered the father of
the modern theory of fractals. I just mention the most known:
 Benoit.B.Mandelbrot,"The  Fractal  Geometry  of  Nature",1982,   Freeman,
San Francisco.


 I  hope you like Smartfractal and  find interesting images that meet your
sense of beauty.
                                                  Simone Avogadro