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FRACLAND Fractal Landscape Generator for the Atari ST.
-------------------------------------------------------
(c) 1992 David Billington
-------------------------
Version 1.2 October 1992
---------------------------
Contents
-----------
1. Introduction.
2. Quick Start.
3. Generating Landscapes.
4. Generating 3D Views.
5. Fracland Modes.
6. Generating Animation.
7. Menu Entries.
FILE
SAVE VIEW
LOAD CONTOUR
SAVE CONTOUR
LOAD STORY
SAVE STORY
LOAD ANIMATION
SAVE ANIMATION
CONTOUR
GENERATE
SHADE
DETAIL
CONTOUR ZONES
COLOURING
3D VIEW
ANIMATION
PLAY BACK
STORY BOARD
PLAY SPEED
MODE
DO RENDERING
Appendix 1. Key and mouse functions.
Appendix 2. Bibliography.
The closing address.
1. Introduction
---------------
The word FRACTAL was coined by Benoit B Mandelbrot in his book 'The
Fractal Geometry of Nature'. It is used to describe objects which exhibit the
property of self-similarity. An object is said to be self-similar if its
structure does not vary under magnification. For example a branch from a tree
has a similar structure to the whole tree, a twig has much in common with the
branch and so on right down to the smallest twigglet. The vast majority of
objects in nature defy definition in terms of circles and squares but it is
readily apparent that they are self-similar. Mandelbrot and his successors have
described several ways in which this property of self-similarity may be
exploited in order to mimic nature. Building from simple algorithms convincing
clouds, trees, coast lines, mountains and many other natural phenomena.
This program 'FRACLAND' is concerned with realistic modelling of fractal
mountains. It goes beyond producing the data which describes the landscape and
allows you to shade it, produce three dimensional views and even generate
animation depicting journeys through your fictitious mathematical worlds.
2. Quick Start
--------------
For those to impatient to read the manual here is the quick guide to
getting a few pictures out of FRACLAND. Before you can really get the best out
of FRACLAND you will need to spend a little time getting to know your way around
the various functions, but producing a simple animation can be done in a few
minutes, as we are about to find out....
P.S. If you have a half meg ST you will need to have a blank formatted disc
ready.
1. Creating a contour map.
-----------------------
Double click on FRACLAND.PRG and at the first dialogue click on the
'Generate' button. Now enter 169 in the 'Random Seed' field and press
return. This will draw a contour map.
2. Drawing a 3D view of the contour.
---------------------------------
Click on the menu entry marked '3D View'. This will display the Key
Frame dialogue, click on the button marked 'Visual'. Use the mouse
to select a view (left mouse button switches between move and tilt).
Once you are happy with the outline press the space bar to return to
the desktop and press return to draw the view. You can switch between
the view screen and the desktop by pressing any key or by left mouse
clicking on the desktop.
3. Generating an animation.
------------------------
Click on the menu entry marked 'Load Story' and selected the file
DEMO.STR which should have been supplied with FRACLAND. Now click on
the menu entry marked 'Do Rendering', this will display an alert
asking whether you want to shade the contour before drawing the
animation. If you click on 'Yes' the animation will look much better
but the calculating the shade data will take about 6 minutes before
drawing commences. If there is not enough room to hold the animation
in memory you will be asked to supply a file name (insert that blank
disk!). The program will now draw 9 frames of animation.
4. Playing an animation.
---------------------
If the animation was not saved to disk then click on the menu entry
marked 'Play Back' to see the results. Press the space bar to exit
from playback.
If the animation was saved to disc then quit from FRACLAND and double
click on FRACPLAY.PRG now click on the button marked 'Load' and select
the file you saved the animation to in FRACLAND. Press the return key
to see the end result.
This should have given you a taste of what FRACLAND is all about, to
improve the image quality try shading, increasing the detail, adding friction
and adjusting the zone heights and colours. I hope you enjoy playing with this
program, who knows you may even be tempted to read the instructions!
3. Generating Landscapes
------------------------
The contour map consists of 16,384 height measurements, this describes
the fractal and as such is the fundamental data set in FRACLAND. Each time a
contour map is to be generated you will be presented with the Contour
Parameters dialogue, this has four items which describe the contour, each
parameter is explained below.
Firstly we must initialise the random number generator by 'seeding' it.
The seed is a four digit number used as a starting point for the random number
generator, thus the same seed will produce the same sequence of random numbers
and hence the same contour (although the contour may be modified by using the
other parameters). It is considered correct etiquette to supply birthdays etc
as a seed values. However for the more pragmatic, a random 'random seed'
may be generated by pressing the button marked 'R'.
The distribution of random numbers may be either uniform or normal. To
produce accurate fractals normal deviation should be used, this produces
rounded and more realistic contours. However setting distribution to uniform
will generate a contour about 5 times as fast. You can set the distribution
by clicking on the small button next to the distribution graph of your choice.
The Fractal Dimension determines the ruggedness of the resulting
contour. For a landscape this must lie between 2 and 3. The fractal dimension
describes how the flat 2 dimensional surface invades 3 dimensional space. At the
extremes a fractal dimension of 2 would produce a completely flat contour and a
fractal dimension of 3 would produce a contour which undulated violently,
effectively filling 3 dimensions. Most earthly landscapes exhibit a fractal
dimension of between 2.0 and 2.4, from rolling pastures to craggy mountains.
The Initial Deviation is the amount by which the contour is allowed to move
above or below the initial flat plane. The default value of 128 gives a good,
lifelike result. Raising the initial deviation will give high mountains and
deep ravines, lowering the value gives flatter landscapes.
The algorithm used to generate the contour is Mid-point Displacement. See
appendix 3 for further reading.
4. Generating 3D views
----------------------
Once a contour has been generated it can be displayed as a 3D projection by
clicking on the '3D View' menu entry. This will display the key frame dialogue.
The left three fields hold the coordinates of the observer (the origin is the
centre of the contour). The three fields to the right hold the pitch, roll and
yaw respectively.
To make the process of setting the view coordinates easier, two visual
methods are available.
1. Clicking on the button marked 'From Map' will allow you to position the
camera and set the line of sight by marking points on the contour map.
After you have used the mouse to select two points a dialogue will be
displayed showing their heights and allowing them to be adjusted. (It is
recommended that you always add about 5 to the height of the camera, this
gives a more natural perspective than having your eye at ground level)
2. Clicking on the 'Visual' button will switch into real time, wire frame
mode. This facility allows the position of the 3D view to be set by
roaming over the current contour using the mouse. The left mouse button
switches between forward/backward and up/down. The right mouse draws a
low detail solid landscape. 'I' switches the instrumentation on/off.
'D' switches the amount of detail. The space bar exits wire frame mode
and places the coordinates of the wire frame view into the key frame
dialogue. For small movements the arrow keys simulate the mouse
movements.
You can repeat either process or edit the values as much as you like,
checking the results in wire frame by using the visual button. Once you have a
satisfactory view you can draw it by pressing the OK button. The drawing
process may be abandoned by pressing the ESC key. The quality of the result
will depend on a) whether the contour has been shaded and b) the amount of
detail set. For more information see the menu entries GENERATE, DETAIL and
SHADE.
5. Fracland Modes
-----------------
For maximum flexibility the animation facilities in FRACLAND have two modes
of operation 'MEMORY' and 'DISC'. The mode determines where the large animation
files are to be held. This information is used by the 'PLAYBACK' and
'DO RENDERING' options. In 'DISC' mode you will be prompted for a file name,
however in 'MEMORY' mode all data will be held in RAM. The mode may be switched
at any time by using the menu entry marked 'MODE'.
'MEMORY MODE' - all animation will be generated in memory allowing it to be
played back at up to 24 frames per second. You can load and save animation but
any attempt to load an animation that is larger than the available memory will
fail. The total number of frames available is displayed when you switch from
'DISC' to 'MEMORY' and the number of animation frames left is displayed at the
bottom of the 'STORY BOARD' dialogue. Unfortunately 'MEMORY MODE' is not
available on 520 machines (save animation to disc and use FRACPLAY instead).
'DISC MODE' - all frames of animation are saved directly to a disc file.
They may be played back straight from disc or loaded into the separate utility
FRACPLAY which can hold approximately 9 more frames of animation than FRACLAND.
It also means that hard disc users can generate very large animation sequences
and play them back at reasonable speed directly from disc (17 frames a second on
my Quantum LP52S). Not all options are available when playing back from disc,
see the entry on 'PLAY SPEED' for more details.
6. Generating Animation
-----------------------
To generate animation FRACLAND must first be given the start and end views,
and the number of frames of animation between the two. It will then calculate a
flight path between these points and automatically draw the intervening frames.
This method of animation is known as TWEENing. The start and end frames are
known as KEY frames, a key frame is a view defined by the animator that MUST
form part of the flight path. You are not restricted to just two key frames, you
can specify up to nine and FRACLAND will formulate a path which visits each in
turn, thus allowing very complex animation to be described. You must also supply
the number of frames it takes to travel between each pair of key frames, in
animation speak this is the number of TWEENS. Thus the number of frames in an
animation is the sum of all tweens. In 'MEMORY mode this total must not exceed
the available memory.
A sequence of key frames and tween sizes in known as a STORY, you can enter
the details of an animation by clicking on the STORY BOARD menu entry. The Story
Board dialogue has nine mountain icons and eight arrows, each mountain icon is
an animation key frame, each arrow holds the number of frames between the key
frames on either side. Clicking on a mountain icon will display the key frame
details dialogue into which the coordinates should be entered, this is the same
dialogue as used to generate a single 3D view and the fields and buttons are
described in the section GENERATING 3D VIEWS. Clicking on an arrow will display
the tween details dialogue, the number of tween frames may be adjusted by
clicking on the dialogue arrow buttons. The end of a story is indicated by a
tween value of 0.
You may copy the coordinates of one key frame to another by using the copy
button, first click on the copy button, then the frame you wish to copy from,
followed by the frame your copying to. Hint - copying the first frame to the
last will make the animation loop smoothly.
Once you have decided on the key frames and tween values you may preview the
animation in wire frame by clicking on the 'Preview' button. This allows
adjustments to be made before committing to a full rendering (you can exit
preview mode by pressing the SPACE bar or the left mouse button). Once you are
happy with the preview you can render the animation by clicking on the 'DO
RENDERING' menu entry. This will display a dialogue detailing the current status
of the render which may be stopped at any time by pressing the 'ESC' key.
7. Menu Entries
---------------
FILE
SAVE VIEW
To save the CURRENT VIEW as a standard DEGAS
picture click on the SAVE VIEW and supply a file name
and path in the file selector. You can display the
CURRENT VIEW before saving by pressing any key or by
left clicking on the desk top.
LOAD CONTOUR
This option will allow you to load contours from disc.
For information on what details are loaded please see
the SAVE CONTOUR menu entry description. Once the contour
has been loaded a short wait will occur whilst the
CONTOUR MAP is redrawn. CONTOUR files should have the
extension '.CON'
SAVE CONTOUR
When you have found a contour that you are happy with
and have decided on the position and colour of CONTOUR
ZONES it may be saved to disc. You may specify the
path and file name in the file selector box, the file
will be given the extension '.CON'. CON files hold
the shape of the contour, colour and zone information,
the amount of detail required and the shading data,
if shading has been done. Saving this information
to disc for your favourite landscapes will save time as
it can take up to 10 minutes to generate, shade and draw
a complex contour. Saved contour files may also be loaded
at startup rather than generating from scratch each time.
LOAD STORY
The path taken through the landscape by an animation
is defined by the STORY BOARD. The details of this path
may be loaded from disc into the STORY BOARD by
clicking on the LOAD STORY menu entry. The appropriate
file may then be selected from the file selector.
STORY files should have the extension '.STR'
If the STORY being loaded has more frames of animation
than can be held in memory the animation MODE will
automatically be switched to DISC. This will mean that
all animation is to be held on disc, not in memory.
SAVE STORY
The current details held in the STORY BOARD may be
saved to disc by clicking on this menu item and
supplying a name in the file selector. The file will
automatically be given an extension of '.STR'
LOAD ANIMATION
Animation may be loaded into memory by clicking on the
LOAD ANIMATION menu entry and specifying the name in
the file selector box. Animation files should have an
extension of '.ANn' where n = 1 for low resolution
and 3 for high. Animation may only be loaded if the
MODE is set to MEMORY. If the MODE is set to DISC then
the option will be offered to switch MODES or you may
play the animation straight from disc by using the
PLAYBACK menu option directly.
This action will fail if the animation was saved at a
different resolution or if it contains more frames
than can be fitted into memory. If the animation does
contain more frames than can be fitted into memory then
using the dedicated animation player FRACPLAY.PRG will
allow more frames to be loaded.
SAVE ANIMATION
Once an animation has been created in memory by using
the 'DO RENDERING' option it may be saved to disc
using this menu entry. The name and path may be given
in the file selector and an extension of '.ANn' will be
added, where n = 1 for low resolution and 3 for high.
The file created will contain each frame of the
animation and the colour information. It may be loaded
back into memory using LOAD ANIMATION, played straight
from disc using PLAYBACK in DISC MODE or loaded into
the separate animation player program FRACPLAY.PRG
CONTOUR
GENERATE
This menu entry is used to generate a fractal landscape.
This is the fundamental set of data from which the
contour map, 3 dimensional views and animation are
generated. The concepts, algorithms and parameters used
to generate a landscape are explained in more detail
under the section on GENERATING LANDSCAPES.
To produce a sample landscape click on the GENERATE
menu entry, this will display the dialogue for the
parameters used in generating the fractal. You can
allow most of these to default, simply enter any number
in the field marked RANDOM SEED and click on the OK
button. Each SEED will grow a unique landscape.
SHADE
Initially contour maps are coloured based on height above
sea level (as in most atlases). However to add more
realism you can shade the contour as though a light
source was illuminating it. This helps to bring out the
relief of the contour. To shade a contour click on the
SHADE menu entry. This will display a progress dialogue
informing you how much of the contour has been shaded.
The process takes around six minutes to complete after
which the contour map will be redrawn shaded. The
shading process may be stopped by pressing the ESC key.
A contour may be saved in its shaded form.
(For those interested the algorithm used is Lambert's
Cosine)
DETAIL
When a 3 dimensional view is generated the number of
polygons drawn governs the speed and detail. The more
polygons the more detail, less polygons gives faster
drawing. This usually means that tests are drawn in rough
until the correct results are achieved when the detail
can be increased to produce the finished article. The
amount of detail can be adjusted by clicking on the
DETAIL menu entry, this will display a dialogue with four
buttons, the further to the left the button selected the
more detail drawn. A view drawn with minimum detail will
take approximately 10 seconds on a standard ST. Maximum
detail views take about 3 minutes each. Thus a 20 frame
animation at maximum detail will take about an hour to
produce.
CONTOUR ZONES
Each contour is divided into land and sea. The land is
further divided into 3 zones. This gives a total of four
areas or zones the size of which may be varied as
required. Clicking on the CONTOUR ZONES menu entry will
produce a dialogue box, the percentage of the contour
divided into sea, zone 1 and zone 3 should be entered.
If the percentages total more than 100 then they will
crowed each other out, in order of precedence - sea,
zone 1, zone 3, zone 2.
Because the zones are based purely on height they
appear as straight lines on the 3D views, this can look
unnatural and to prevent it you may specify the percentage
of friction to be used when drawing zones 1 and 3.
Friction on a contour will mean that zones 1 and 3 will
'invade' the flatter areas of zone 2, just as snow
will gather on flat ground at lower altitudes or trees
colonise higher ground if not to steep.
The contour zones set are also used when producing 3
dimensional views.
(N.B. The only option available to mono users is to
adjust the SEA LEVEL)
COLOURING
Each of the four zones and the sky is assigned a range
of colours. Clicking on the COLOURING menu entry in
low resolution will display the Zone Colours dialogue.
The colour of the sea may be set by selecting either Sea
or Ocean; the sky can be set by selecting Night, Blue Sky,
Hazy or Tropical. To change the colour of a land zone
first click one of the Zone buttons then choose a terrain
type from the array of buttons below. All changes to
the colours are instantly reflected in the colour bar on
the top right of the dialogue (except the sky colour). To
observe the effect of your colour changes you can
display the last 3D view generated by clicking on the
View button. (This will be a blank screen if no view
has been drawn). Although the ST only provides a palette
of 16 colours they are stippled to produce a total of 46
virtual colours.
Clicking on the COLOURING menu entry in mono will
provide a dialogue to allow the background colour of 3 D
views to be selected as black or white.
3D VIEW
The current contour may be drawn as a 3 dimensional
projection. To produce a single 3D view you must click
on the 3D VIEW menu entry. This will display a dialogue
for the coordinates to be used and options to set them
using visual methods. For more detail on creating 3D
images see the section on GENERATING 3D VIEWS. Once
you are happy with the coordinates you can click on OK
to start the drawing process or CANCEL to abandon.
Clicking on OK will draw a progress report dialogue, when
the transformation and sort have finished the screen will
be switched to the CURRENT VIEW screen and the landscape
drawn. The process may be stopped at any time (except
during the sort phase) by pressing the ESC key.
ANIMATION
PLAY BACK
Animation can be played using this menu option. In DISC
MODE clicking on PLAY BACK will produce a file selector
into which the name of an animation file (.ANn) should be
entered. The file will then be played direct from disc.
In MEMORY MODE the animation will immediately start
playing. If no animation is held in memory then a
warning will be given. The speed and direction of the play
back can be set using the PLAY SPEED menu entry detailed
below. You can stop an animation playing by left mouse
click or pressing the space bar.
You may also use the program FRACPLAY.PRG to play
animation generated by FRACLAND. FRACPLAY can generally
hold 9 more frames of animation in memory than can be
stored by FRACLAND.
STORY BOARD
To create an animation the path the 'camera' takes through
the landscape must be defined. The STORY BOARD menu entry
will display a dialogue box into which this path may be
entered. For more detail on the concepts involved see the
section on GENERATING ANIMATION.
PLAY SPEED
The speed and direction an animation is played back may
be set by clicking on the PLAY SPEED menu item. This
will produce a dialogue. The entry marked SPEED (initially
set to 5) may be edited to give the delay used between
frames. 0 is the quickest at around 24 frames a second
from memory. Direction can be set to forward or reverse
and the animation mode may be LOOP or PING. If the
animation is to loop it will return directly to the start
frame on reaching the end. In ping mode on reaching the
end it will replay the frames in reverse order. Pinging
can produce a smoother animation sequence without a sudden
chop at the end.
(N.B. Only the speed has any effect in DISC MODE)
MODE
FRACLAND may be used in two modes DISC or MEMORY. The
mode dictates where animation is held. For more
information see the section on FRACLAND MODES. The MODE
may be changed at any time using the menu entry MODE. If
you try and switch to MEMORY MODE with more frames of
animation in the STORY BOARD than can be held in memory
an error will be given requesting the number be reduced.
Otherwise the number of frames that can be held in memory
will be displayed in an alert box.
DO RENDERING
This menu entry draws the frames of an animation.
Once all the details of the animation sequence have been
entered into the STORY BOARD you can click on this option
to begin drawing the 3D animation frames. Each frame
is preceded by a report dialogue which will indicate
how many frames have been drawn, how many are left
and the progress of the frame currently being drawn.
Each frame will be written to disc or memory (depending
on the current MODE) after it has been drawn, ready to be
played back on completion. The rendering may be stopped
at any time by pressing the ESC key. If you have not
shaded the contour you will be given the opportunity
to do so before rendering commences, for more detail
on shading see the information on the SHADE menu entry
above. For more details on how to create animation
see the section on GENERATING ANIMATION. Please note that
the quality of the animation is dependant on the amount of
detail drawn, this may be set using the DETAIL menu entry.
Appendix 1. Key and Mouse Functions.
----------- ------------------------
From the desk top.
------------------
ESC Abandons current process.
ANY KEY Switch the screen between displaying the GEM desk
top and the CURRENT VIEW.
LEFT MOUSE BUTTON Left clicking the mouse over any empty area of the
desk top also switches screens between GEM and the
CURRENT VIEW.
From wire frame visual mode.
----------------------------
LEFT MOUSE BUTTON Switch mouse function between moving
forward / backward and looking up / down.
RIGHT MOUSE BUTTON Draw a low detail solid render of the current view.
MOUSE UP Move forward / look up.
MOUSE DOWN Move backwards / look down.
MOUSE LEFT Turn to the right.
MOUSE RIGHT Turn to the left.
SPACE BAR Exit visual mode.
D Switch between high and low detail.
I Switch instrumentation on/off.
H Home the view.
ARROW KEYS Provide the same function as the mouse directions for
fine detail.
From wire frame preview mode.
-----------------------------
LEFT MOUSE BUTTON Exit preview mode.
SPACE BAR Exit preview mode.
D Switch between high and low detail.
I Switch instrumentation on/off.
During play back.
-----------------
LEFT MOUSE BUTTON Exit play back.
SPACE BAR Exit play back.
Appendix 2. Bibliography.
----------- -------------
1. The Science of Fractal Images.
Peitgen, Saupe (editors)
Published by Springer-Verlag 1988 ISBN 0-387-96608-0.
2. Computer Rendering of Stochastic Models.
Fournier, Fussell and Carpenter.
Communications of the ACM Volume 25 Number 6 (June 82)
3. Chaos
James Gleick.
Published by Cardinal ISBN 0-7474-0413-5.
4. Real-Time 3D graphics for the Atari St.
Andrew Tyler.
Published by Sigma Press ISBN 1-85058-217-3
The closing address.
--------------------
I hope you enjoy using FRACLAND its been fun writing and researching it.
Watch out for new versions with PHOTOCHROME 19200 colour support, much larger
contour maps and all sorts of other bits, when time (currently fully occupied by
a two month old daughter) allows.
Please write with comments, enhancement ideas, bug reports and information
on other fractal programs to :-
David Billington
55 Church Street,
Hadley,
Telford,
Shoropshire,
TF1 4RQ
P.S. Why the fish shaped mouse ? Its a bit of christian symbolism. Fractals are
ok but God does a much better job.
human was the music,
natural was the static ...
- John Updike
--- The End ---