Copyright: © 1989-99 Thomas Hövel


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Index
WinCIG Chaos Image Generator

Calculates Apple Set fractal images

Quick Reference - the most important information on one page

The Concept of this Program

"Speed is no witchcraft"

(Hardware Requirements and Tips)

Basic Information About Apple Men

Dive Into the World of the Apple Men

The Menu Items and Dialogues:

Menu File:

Save as

Load

Bitmap Export

Menu Range:

Range

Iterations

Reset Initial Range

Automatic Zoom

Range + 10% (Context Menu)

Range + 25% (Context Menu)

Range + 50% (Context Menu)

Range + 100% (Context Menu)

CPU Fixed

FPU Single

FPU Double

FPU Extended

Menu Display:

Display

Default Window Size

Colour Palette

Previous Colour Palette

Next Colour Palette

Context Menu (right mouse click over image):

Center This Point (Context Menu)

Range + 10% (Context Menu)

Range + 25% (Context Menu)

Range + 50% (Context Menu)

Range + 100% (Context Menu)

Please visit my web-site at

http://www.th-soft.com/a

or

http://www.hoevel.de/a

If you have a problem with WinCIG and can't solve it at my web-site, please contact me at wincig@th-soft.com and report your problem.

© 1999-2000 Thomas Hövel Software (Impressum / Support)


Quick Reference

Basic information on one page

This program turns a simple mathematical formula into fascinating images - provided, you select interesting ranges!

Automatic Zoom

Wait till the message "Calculating ..." disappears from the window caption. Then hit F12 to start Automatic Zoom. The computer selects a new range and calculates the image.

Normally you reach very interesting images after using Automatic Zoom between 10 and 20 times.

Hit F4 to return to the start-up range and start a new session of Automatic Zooming!

Note: The message informing you that the current image exceeds the accuracy of the FPU Double type also means that you are close to the limit of accuracy. You can still use Automatic Zoom a few times; hit F4 to start again when the image becomes glitchy!

Note: Automatic Zoom is only available when the computer finished calculating. Most other functions are also available during calculations!

Manual Zoom

Click the left mouse button on the upper left corner of the region you want to magnify. Then move the mouse to the right and to the bottom till the desired area is highlighted.

When you release the mouse button now, a dialogue with details about the selected range pops up. Select OK to magnify the range; or click Cancel to select a different region.

Dive Into the World of the Apple Men

Colour Selection

Hit F9 to open a dialogue that shows the available colour palettes.

Or even better: Hit F8 (next palette) or F7 (previous palette) several times to cycle through the available palettes.

More Information About Colour Palettes

Saving and Loading Ranges

Hit F2 to save the co-ordinates of the current image. You specify a name for this image.

Hit F3 to load co-ordinates. Choose among the available co-ordinate settings. Several saved co-ordinates come with the program - have a look!

Select "Bitmap Export" from the "File" menu to save the current image as a Windows Bitmap file - you can use it as your Desktop Wallpaper!

Specifying Image Size / Creating Desktop Wallpapers

Hit F11 to open the image size dialogue.

Large images require more memory and calculation takes longer (proportional to pixels in the image).

Also mind the required memory - this should be several megabytes less than the physical memory available in your computer.

Use "Free" for image sizes that are not in the list. The default for Free is the current display size - ideal for creating Desktop Wallpapers!

Select "Bitmap Export" from the "File" menu to save the current image as a Windows Bitmap file; save it in the Windows directory. If you are using Windows 95/98 or NT 4.0, select Control Panel, open Display and select the new image as Wallpaper on the Background page.

Links

The Concept of this Program

"Speed is no witchcraft"

(Hardware Requirements and Tips)

Basic Information About Apple Men

Dive Into the World of the Apple Men


The Concept
The Concept of WinCIG

This program calculates and displays Apple Men (also known as Mandelbrot Trees).

This requires calculating thousands of arithmetical operations for hundreds of thousands pixels. And this can take some time!

(Background information: Basic Information About Apple Men)

To make the delay appear shorter, WinCIG employs two new concepts:

1. Interlaced Calculation of Image Lines

You may know this concept from the Internet: images appearing interlacedly.

It's slightly different with WinCIG because the old image remains partially visible, resulting in a line by line transition.

2. Interlaced Calculation of Iterations

Normally programs calculate hundreds of iterations for one point before processing the next point.

WinCIG can interrupt calculations for any point at any time. This allows the program to calculate a full image with few iterations to start with, while calculating more details later on.

Zooming Into Images

The program allows you to select part of the image as the range for a new image. Simply click the upper left corner and move the mouse to the left and to the bottom while holding the mouse button down.

Release the mouse button to magnify this area.

Move the mouse to the top or to the left till the frame disappears to cancel this operation.

The program will automatically adjust the initial iterations value for the new image.


Hardware Requirements
Hardware Requirements and Speed

This program should run on any computer that satisfies the hardware requirements of Windows 95/98 or Windows NT (i386).

But two factors can make this program run very slow!

1. Slow Performance Without Floating Point Unit

The Floating Point Unit (FPU, aka Numerical Co-Processor) is part of all modern micro-processors. For older processors (e.g. 80386, 80486SX) it is a separate chip that can be installed optionally. (The 80486DX includes an FPU.)

The FPU has no effect on calculations using the type "CPU Fixed". Calculations using the types "FPU Single", "FPU Double", or "FPU Extended" will be very slow on computers without FPU.

2. Not Enough Physical Memory

The programs stores status information for every pixel. The amount of memory required depends on the size of the image and the numerical type used.

The Display dialogue shows how much memory will be needed.

The required memory should be several megabytes lower than the physical memory.

Calculation Time is Proportional to Number of Pixels!

To dive into the world of Apple Men, you can choose a low resolution (e.g. 320x240 or 400x300) and use the "Show Image in Double Size" option.

If you found an interesting area and want to save the image, switch to the resolution you want (e.g. current screen resolution) and calculate a fully detailed image.

At least 256 colours required

Most Colour Palettes require a display mode with at least 256 colours (see Colour Palettes).

For optimal results, use a display mode with at least 32768 colours (15 bit).


Information about Apple Men
Basic Information About Apple Men

The program uses a formula found by Benoît B. Mandelbrot. It looks pretty simple at first glance:

For a point with the co-ordinates c, the following sequence will be calculated:

f[0] (c) = c

f[i+1] (c) = f[i]^2 + c

This continues until |f[i](c)| > trigger or i > limit.

i then specifies the colour of the dot on the screen.

c is a complex number. Unless you are using C++, this simple formula is not quite so simple to implement.

The routines for the type "CPU Fixed" were implemented in Assembler.

I calculated the first Apple Men images using BASIC programs on Z80 computers - this must have been in 1986. The calculations took several hours for one image!

Things improved quite a lot when I implemented the first fixed arithmetic routines in Z80 assembler: calculations "only" took about one hour per image!

The Z80 is a 8 bit processor that can add and subtract, but cannot either multiply or divide!

In 1991 I wrote a PC version using 80386 assembler code. Fixed arithmetic where implemented using the processors 32 bit operations (including multiplication).

In the VGA 256 colour mode (320 x 200 pixels), calculating an image only took 2 through 4 minutes!

Calculations actually were so fast, that you could easily reach the limits of my fixed arithmetic.

One had the choice to continue using floating point routines - but those were about 20 times slower (which means about one hour per image again).

1998 saw early versions of WinCIG. Besides the trusty fixed arithmetic it supports three FPU formats.

Using a low image resolution you can quickly dive into the fascinating world of the Apple Men.

And it takes very long till you reach the limits of the FPU Extended type!!!


Dive Into the World of the Apple Men

Here you see the basic Apple Men image:

Interesting areas to zoom into are the grey regions around the big black Apple Man.

The red frame indicates the area that is magnified below.

To magnify an area, just click on the upper left corner and move the mouse to the bottom and to the left while holding down the mouse button.

Release the mouse button to magnify the selected area. The dialogue "Range" will show up where you can adjust the values calculated by the program. Normally you can use these default values.

Move the mouse back to the top or to the right till the frame disappears to cancel.

Here is a magnification (the range indicated by a red frame in the image above):

Another Apple Man shows up in the middle.

When diving into the world of Apple Men you will find quite often that magnified areas look similar to the previous image.

Images here are only black and white to keep the help file small.

Just try it: it even looks better in colour!


Automatic Zoom

You can reach this function using "Automatic Zoom" in the "File" menu or hitting F12.

This function is available only when the computer finished calculating the current image (wait till the "Calculating ..." message disappears from the window caption).

The computer will select an "interesting" area of the current image and zoom into it.

"Interesting" is solely based on a mathematical formula.

This function will only work if there are pixels in the image that reach the maximum iteration level. This is always true for ranges reached using the Automatic Zoom function.

Hit F4 to return to the start-up range and start a new series of Automatic Zooming!


Dialogue "Range"

You can open this dialogue using "Range" in the "File" menu or hitting F5.

It also appears if you select a region using the mouse.

All images displayed by this program are a region of the plane of complex numbers - x-axis shows real part, y-axis shows imaginary part.

You can enter these co-ordinates in this dialogue.

The values will be calculated automatically when you're using the mouse to zoom into an existing image.

The details of the image depend on the iterations calculated.

Start and Incr. only affect the intermediate images calculated. The final image depends on the End value for Iterations only.

The program calculates default values when you use the mouse.

You can use higher values for Iterations End at any time using the "Iterations" dialogue (via "Iterations" in the "File" menu or by hitting F6).


Dialogue "Iterations"

You can open this dialogue using "Iterations" in the "File" menu or hitting F6.

It displays the current value for Iterations and allows you to enter a higher limit.


Dialogue "Display"

You can open this dialogue using "Display" in the "File" menu or hitting F11.

This dialogue allows you to specify the size of the image calculated.

For speedy calculations you can choose a small image size and have it displayed in double size.

Note: an image sized 800 x 600 contains four times as many points as an image sized 400 x 300 (which will be 800 x 600 on the screen when viewed in double size).

This can save a lot of time when you are searching for interesting areas!

Select "Free" to specify image sizes not in the list.

The default setting is the current screen resolution - ideal for desktop background images!

Currently you can enter sizes between 2 and 4095 pixels.

The OK button will be disabled if you select an image size that won't fit into virtual memory. You can increase virtual memory by resizing your swap file.

Note: Calculations are very slow if the required memory is close to or larger than the amount of physical memory.

The dialogue also shows you how much memory the program requires for the calculation (this is not the size of the bitmap file!) and how much physical memory your computer has.

See also:

"Speed is no Witchcraft"

Dive into the World of Apple Men


Default Window Size

WinCIG tries to adjust the size of its window to show the image without scroll bars; window size is adjusted automatically after program start and when changing the size of the image (see also Display).

Use this function to return to the default size any time you like.


Dialogue "Colour Palette"

You can open this dialogue using "Colour Palette" in the "File" menu or hitting F9.

You can also change the colour palette using the menu items "Next Colour Palette" (Key F8) and "Previous Colour Palette" (Key F7).

The impression of an image depends strongly on the number of colours in the colour palette.

You can see this if you hit F8 several times to cycle through the available colour palettes.

You can use SHIFT+F7 and SHIFT+F8 to shift the colours within the colour palette.

You can use CTRL+F7 and CTRL+F8 to shift the colours within the colour palette using larger steps.

If you hold down one of these key combinations, you can even create animation effects.

You can use these keys to select the colour that dominates an image.

If WinCIG uses the Modulo function to determine the colour use for a pixel, then you can control how often the colour will change within the image.

Using the key combinations ALT+1 through ALT+0 you specify that the colour will change after n iteration levels where n is the number you press along with the ALT key (0 stands for 10).

Using the key combinations CTRL+1 through CTRL+0 you specify that the full palette will be visible n times where n is the number you press along with the CTRL key (0 stands for 10); this function is available only after WinCIG finished calculating.

Iteration levels and Modulo function surely sounds mathematical - and it may sound Greek to you ...

You can try all the various colour palette options without understanding the mathematical background!

See also:

Dive into the World of Apple Men

"Speed is no Witchcraft"


Dialogue "Save as"

You can open this dialogue using "Save as" in the "File" menu or hitting F2.

You can save the image co-ordinates and the iteration settings using a name of your choice.


Dialogue "Load"

You can open this dialogue using "Load" in the "File" menu or hitting F3.

Select from the available settings.

Co-ordinates and iteration settings will be loaded.


Reset Initial Range

You reach this function using "Reset Initial Range" in the "File" menu or hitting F4.

The computer will display the image it automatically calculates after starting the program.


Bitmap Export

Select "Bitmap Export" from the "File" menu.

Choose directory and filename.

The current image will be saved in the Windows Bitmap format (.BMP file).


Numerical Formats

CPU Fixed ("File" menu)

This fixed point format requires 4 bytes per number which makes it the smallest format along with FPU Single. Precision is also very similar to FPU Single.

This is the only format that is always executed by the CPU; it is the fastest format on computers without Floating Point Unit (FPU).

FPU Single ("File" menu)

This floating point format requires 4 bytes per number which makes it the smallest format along with CPU Fixed. Precision is also very similar to CPU Fixed.

This format is very slow on computers without Floating Point Unit.

It should be the fastest format on computers with Floating Point unit.

FPU Double ("File" menu)

This floating point format requires 8 bytes per number.

This format is very slow on computers without Floating Point Unit.

FPU Extended ("File" menu)

This floating point format requires 10 bytes per number.

This format is very slow on computers without Floating Point Unit.

See also:

"Speed is no witchcraft"


Center This Point
Center This Point (Context Menu)

You find this menu item in the context menu if you click the right mouse button anywhere in the image.

Select this menu item to make the clicked point the centre of the new image.

The range is adjusted to make the selected point the centre of the new image.

See also: Increment Visible Range


Increment Visible Range
Increment Visible Range (Context Menu)

You find these menu items in the context menu if you click the right mouse button anywhere in the image.

The visible range will be increment.

The range that is currently visible will still be visible in the new image, but it appears smaller since the range is incremented.

Choose one of these options:

Range + 10%: The visible range will grow 5% on each side (10% in each direction).

Range + 25%: The visible range will grow 12.5% on each side (25% in each direction).

Range + 50%: The visible range will grow 25% on each side (50% in each direction).

Range + 100%: The visible range will grow 50% on each side (100% in each direction).


Impressum

© 1999-2000 Thomas Hövel Software

Saturnstraße 45

53842 Troisdorf 22

Germany

Europe

Please visit my web-site at

http://www.th-soft.com/a

or

http://www.hoevel.de/a

If you have a problem with WinCIG and can't solve it at my web-site, please contact me at wincig@th-soft.com and report your problem.

All Rights Reserved!