Instructions for using QuasiG V1.4 - a freeware Penrose
tiling program that will show and print full-colour Penrose tiling
patterns, and more general quasi-crystal patterns, on any Windows
95/98 or NT/2000 PC.
Using QuasiG is meant to be simple. It has default input values
that will produce a simple image of penrose tiling. Experiment with
the various options to see what they do (example images on the QuasiG page include a summary of the
options in the title bar, so you might like to try creating them to
prove your installation worked).
If you're not familiar with Weeks's quasi.c, just download
QuasiG and play around a bit !!
QuasiG options are accessed
through its Tiling Options Dialog pop-up. This dialog appears when
you run the program, and whenever you access the File/New menu
Depending on options selected, you may be presented with a
series of color dialog popups. These are for selection of Penrose
Dot color, Penrose Line Color, and color code for each unique tile
The program then calculates the pattern, and displays it in a
scrollable window that's 32 cm by 32 cm. If Penrose Tile marking is
selected, with large number of generating lines, or a slow
computer, expect significant delay.
You can open up new tiling windows by File/New - and your
previous options become the default selection for the new window.
This makes it easy to make just small changes from one plot to the
Degrees of Symmetry - Choose an odd number. For example, 5 for
penrose tiling. Rhomb angles will divisible by p / 5. Higher numbers can be interesting.
Generating Lines - choosing more of these makes the pattern
larger. You can choose really small numbers like 5, 7, 9 ... to see
how the construction process works. QuasiG has options to scale the
tiles down to ensure they fit on the scrolled view.
Offset Multiplier - a factor that changes the offset of the
generating line sets, and thereby changes the pattern quite
significantly. For example, try 0.1, 1, 10, etc.,.
Center of Pattern - tick to include only central tiles in the
pattern. Tiles which do not adjoin at least two others are omitted.
For 5-fold symmetry, you get a central decagon shaped pattern.
Fill On - tick to have tiles filled with user-selected color.
You will be prompted for a choice of color for each differently
sized tile (one for fat, one for thin).
Double Colors - tick to have tiles filled with two colors used
for each sized tile. This is Weeks' filling option, and gives two
colors for each tile shape that seem to get allocated
alternately as you radiate out from pattern features.
For this option, when you choose colors, you a really just
defining Hue and Saturation - lightness is determined in the
algorithm as one of two shades for each size of tile.
Gradient Fill - tiles are filled in a variant of the Double
Color method. Lightness is varied amongst the same sized tiles (in
a cycle length equal to the degrees of symmetry). This tends to
hide the symmetries in the pattern - but I liked the look of the
results it gave; and so did curious onlookers passing by my desk.
For this option, when choosing colors, you are also just defining
Hue and Saturation.
Rotate x==y - just exchange x and y directions. Most decent
bitmap editors (e.g. PaintShop Pro, Corel Draw) will do this sort
of thing and more !
Tile Edge Black - ticked means edges of tiles drawn in black. If
cleared, tile edges drawn in same color as tile (so they
Penrose Match Marks - each tile is inscribed as per Fig 1
above. If marks don't line up in a pattern, it's not a penrose
Not Lines - tick to get arcs inscribed in fat tiles as per Fig 1
above. Otherwise, get lines across the fat tiles. Defaults to
Auto Zoom Out - if set, QuasiG
determines the overall size of the pattern, then scales it back to
fit within MS Windows' limits (roughly +/- 16 cm of origin). If
clear, no scaling is done - you get to see just the 32 x 32 cm
subset of the pattern that's centered on the origin. QuasiG's
rhombs have 1 cm length sides.
Magnification - allows you to specify a magnification factor. If
less than 1, the pattern is shrunk (zoomed out). If larger than
one, pattern is enlarged (zoomed in).
Quadrants to Plot - push-button selections determine which
quadrants of the cartesian plane are plotted.
Start Tile - default is 0 - meaning omit no tiles from display.
10 means do not plot first 10% of tiles etc.,. Useful if you want
to isolate a subset of tiles.
End Tile - default is 100, meaning tile plot ends at last tile
generated. 90 means do not plot last 10%, 80 selects out the last
Writing Delay - non-zero value will cause CPU to spin it's
wheels in between drawing successive tiles - thereby slowing down
the drawing process (so you can see what's happening !)
Penrose Dot Color Dialog - choose, or mix a custom color for use
in the fat tile narrow vertex (dark color in Fig 1). The lighter
dot used in the thin tiles gets the same color as the lines
Penrose Line Color Dialog - choose, or mix, a custom color for
use in the lines (arcs) across the width of the fat tiles.
QuasiG can show variants of
quasi-crystal tiling that are different to the one chosen by Eric's
algorithm, such as ones with stars made of a cluster of ten thin tiles ( I first made one like this with Eugenio
Durand's QuasiTiler web site, then experimented with Eric's
code to get it to make something similar)
You might find it necessary to increase the number of lines used
in the generator if you increase the offset multiplier factor much
Eric's quasi.c defaults are equivalent to OffsetMult = 1.
Choosing patterns other than Erics' standard results in no obvious
focus, and other interesting higher-level patterns (see
QuasiG has a number of co-ordinate
reporting and tile identification features for help in
understanding the tile drawing sequence (try mouse right click on a
completed drawing, maybe using a small number of generating lines
eg 5, then watch what happens when you increase the number of
QuasiG can reveal some interesting
patterns not shown in quasi.c:
it can plot all four quadrants of the cartesian plane, and not
just the small segment revealed by Weeks's quasi.c.
this larger plot shows limits in the tiling pattern, and some
assymetries in the pattern.
For example, with 5-symmetry, you can get a central decagonally
shaped tiled region (more evident for larger line sets), with color
coding that reveals "lines" running through the pattern that divide
it into segments of a pentagonal star (choose, say, offset
multiplier 10) ; these remind me of the worms Conway describes in
Penrose patterns, but may be something different.
non-continguous tiles can be seen to be distributed out to the
points of a decagonal stars (two five point stars) that can be
superimposed over the central pattern.
Many of the lines running through the default pattern converge
on a point in the 3rd quadrant that looks quite different to most
of the pattern and which draws your focus.
I'm no maths prof, so I don't know what these mean ! But
my guess is they're evidence of periodicities that mean the pattern
does not satisfy the Penrose matching tests.
an auto-zoom scaling option that allows the full extents of the
plot to be viewed, or you can use hand-entered magnification
Start Tile (as % of Tiles) and End Tile option allows selection of
drawing of a range of tiles, which can be used to build animations
of the drawing process (see animation
The mid-point connecting options available in quasi.c have not
been implemented - my main interest was in looking at the more
You can have up to 500 generating lines - but beware that you
would need > 110 Mbyte of virtual memory to run a 500 line
example, and could run out of memory (e.g. if your disk with the
swapfile hasn't enough free space).
QuasiG also uses a different
drawing order to Weeks's Unix program. Weeks's program plotted
tiles from the center of the pattern outwards - this is probably
best if plotting on an x-y plotter, but not needed for Screen
display and page-display printers. So QuasiG justs plots the tiles
in the order they are generated. I found it interesting to watch
the tile generation (minimize/maximize the window for
action-replays!), and included a delay option to slow down the
drawing process. This can be helpful if trying to understand the
QuasiG displays it's output in a
scrolling window that extends +/- 16 cm either side of the origin,
and has an auto-zoom scale (Magnification) feature that will set
the magnification at a figure that allows the whole pattern to be
viewed. You can use the File/New option to open additional windows
- Tiling Options will default to your last choice.
Tile Marking was a new feature in QuasiG V1.3. It's useful for investigating the
sequence in which tiles are drawn. Read further only if you're
curious about how it works...
The Status bar identifies the Tile
No of the tile under the cursor. The Tile No is its index
(or order) in the generating sequence; if the cursor is not over
any tile, the Tile No will be one more than the maximum number of
Tiles can be marked by clearing
their colour, as an aid to identifying the drawing progression.
Mark an individual tile by left clicking on it - it's colour will
be cleared. If you mark a second tile, the Skipped Tiles box of the status bar reports how
many tiles were drawn between the last and previous tiles. This is
not how many lie between them on the tiled plane - rather it is how
further along in the generating sequence the tile occurs.
The Status bar now includes reporting of the (x,y) coordinates
of the cursor. Coordinate axis can be superimposed on the image, by
using the Tile Marking Pop-up Menu
item Draw Axes. To activate the Tile
Marking pop-up, right click the mouse anywhere on drawing.
The tile drawn immediately after a marked tile can be identified
by Tile Marking menu Next Tile
function. This can be repeated to show successive tiles, but only
the last S tiles remain marked (where S is the Degrees of
Symmetry). Prev Tile marks the
previous tile in the sequence
The Tile Marking menu Next Row function identifies the tile
drawn in the next row (there are 2 * S tiles per row).
Prev Row goes tothe previous
You don't need to understand a word of the
next two sections in order to use QuasiG. These words are for the
techo types out there...
QuasiG is written in Visual C++
V6.0, as a 32 bit MDI application using MFC classes. It was my
first attempt at writing such an application, and does some unusual
things - like popping up its configuration dialogs before you've
seen a main window frame, and maximising the document window (you
can use the Window/Cascade or Tile options to change the latter
after the windows open).
QuasiG generates the tiles to
memory (rather than directly to display). It uses the MFC CArray
class which dynamically allocates space for tiles; the memory is
released when the display window is closed - and varies in
proportion to s/2*(s-1)*l^2 where s=symmetries, and l=lines. It can
be interesting to plot the Windows 95 System Monitor's memory
manager items while running QuasiG. It also gives your graphics
adaptor a pretty serious workout (when running in colour fill
mode), and can stree remote login software like RAdmin, TNG
Unicenter and PC Anywhere.
If you understood this techno-talk, you might be interested in a
copy of the SourceFilter programming utility.
Printing with many browsers (including IE5.5 and earlier) often
doesn't work real well because most browser print functions don't
handle the horizontal scrolling view you get on screen. This page
has been put together to facilitate printing the text on an A4 page
- essentially you will see everything within the white area of the
However, many of the images extending outside this area will get
clipped out. You could try changing your print setup options to
select landscape printing layout (but they'll mostly be split
across a page).
If you really want to print the images, make them with QuasiG
and print directly from its File/Print menu item. This will print
the screen image across 4 A4 size pages (A4 tiles !) - the screen
plot area is 32 cm by 32 cm, and prints isometrically (1 cm of
screen = 1 cm of page).
19th June 2001, Last Revised 24th Jan 2017
Last Revision: Relocated to new host, some broken links updated
This material may be used for educational non-profit purposes
with proper acknowledgement of the source. If any images created
with QuasiG are posted on the net, send me the link url. All other
uses, please email email@example.com