The following gallery of graphs demonstrate the visual range
of graphs that GrafEq can produce.
There is also a rogue’s gallery
of troublesome graphs.


These graphs are possible because of the expressive power of general implicit relations.
Each graph has a short description of why it came to be,
as well a link to the defining equation and larger views.
Interested GrafEq users can generate portions of the graphs at any resolution using GrafEq;
many of them are included in the downloadable demo.
We invite users of other graphing packages to try some of the graphs as well...



Margarita
This graph adorns the front cover of the GrafEq 2.02
manual. It shows seven spirals trying to live
within a “square” grid. Two colours were used
because of the impending two colour printing process
for the manual cover.
The red component emphasizes the graph’s spiral nature.



Masked
Found partially by luck, this is the GrafEq
mascot. I am uncertain whether this shows more about
the anthropocentric nature of human vision
or the expressiveness of reasonably simple implicit relations.


Simply Spherical
This graph adorns the back cover of the GrafEq 2.02
manual. Although GrafEq 2.02
only presents two dimensional views of graphs, three dimensional
graphs such as this can be fudged by modelling the half toning
process within the equation.



Decimal Squares
This graph shows the square integers in base ten.
It is an example of a graph based on an enumeration;
GrafEq 2.10 handles these sorts of graphs much better than earlier versions of GrafEq.


Forest’s Edge
A graph expressly made up to demonstrate the colour capabilities of
GrafEq—in particular, the layering of several colour graphs.
GrafEq users can see how contrived the graph is by zooming out.



Digital Bacteria
One of the earlier graphs to use colour in a visually effective
manner, it was created as a demonstration graph for version 2.00.
The “digital” portion of the bacteria was also used to test
parts of the internal workings of GrafEq 2.00.


Disc 9
The first halftoned graph created using GrafEq.
Prominently shown on the front of our colour brochure for
version 2.01, this was made shortly after I realized that halftoning
was possible.
Close scrutiny will reveal that the half toning pattern used is more geometric than the
mathematically simpler one used for the more recent Simply Spherical.



Frontispiece
This graph, reminiscent of wroughtiron work, has
been front and center on early versions of the
manual for the second version of GrafEq. The latest version sports a slightly different
graph
which lacks the calligraphic strokes
present in earlier versions  the strokes are shaved away by
the subpixel refining added in version 2.02.
Artists may prefer to retain the strokes by disabling subpixel refining.


Sunlight Revealed
A cheery exposition of GrafEq’s
blending capabilities. Three coloured layers (red, blue, and yellow)
are present along with the white “sunlight” layer.
GrafEq users can try varying the colour scheme of the primary layers
from Manhattan blues to Arizona tans.



Chrome
The first gallery picture produced with GrafEq 2.03.


Jupiter’s Dawn
A moderately simple graph which exhibits both one an
two dimensional regions. The graph is given using the
generalized max operator.



Threesome
In the full view, a clear mind can see the three beings.
This graph was conjured up by combining several translated
concentric patterns using a XORlike operator.
GrafEq users can see the individual pieces by removing
factors from the defining equation.


Arachnid
A stark, if somewhat unfriendly graph made up shortly after
I started experiencing “apartment life”.
Needless to say, this graph helped strengthen my resolve
to completely eradicate all unwanted guests.
Fastidious cleaning has resulted in not seeing any of these sorts of
guests since moving in.



Cracked Flowers
Created after an autumn afternoon stroll through a local park.
The lower right gives away its heritage, while the upper left
speaks of its creation.


Plaid Meltdown
A halftoned graph showing both a regular and irregular pattern.



The Big Swim
Some find this graph fascinating for
the variety of pleasing, smooth shapes generated by a single, simple equation.
Modifying the equation seems to needlessly complicate
both the graph and its definition.
