OghamStars Wiki
Draw stars dynamically & adjust draw parameters in real time. Fun!
Brought to you by:
tomchenhall
Menu
▾
▴
Home
Welcome to your wiki!
This is the default page, edit it as you see fit. To add a new page simply reference it within brackets, e.g.: [SamplePage].
The wiki uses Markdown syntax.
Project Members:
- Thomas L. Chenhall (admin)
These stars are really ancient symbols, nobody can say who discovered them.
OghamStars source .fla file has been posted for transparency reasons.
OghamStars 1.02 Help
December 28, 2020
Contents:
1) Getting the software running
2) 'X' Field and Compute Button
3) Monochrome Mode
4) Opacity Slider and automation
5) Color Adjust Slider and automation
6) Line Thickness Slider and automation
7) Color Selection Buttons
8) Layering Mode Button
9) Display Equations
10) Clockwise / Counterclockwise Draw Switch
11) Draw Speed Adjust Slider
12) Pause Button
13) Preserve Symmetry Switch Button
14) Lines Drawn Count
15) Background Selector
16) Keyboard Shortcuts
17) Zooming and Printing at maximum resolution
18) Hallucination Warning
19) Educational Purpose
This software was coded in Flash 8, and will run using any Flash player that was released after 2004. Your system may warn you with a security alert when you try to run it. On a mac you have to go to your security system preferences to allow it to run. Two exe files and two mac applications are available as stand-alone applications, but nothing for your smartphone. I include a legacy version compatible with Windows XP and a legacy Mac PPC version to be fair, but those with newer computers may need to find a 64-bit Flash Player. Those who have used my other softwares hopefully have already downloaded this. Since Flash is being 'ended' by Adobe shortly, its unlikely that the Flash plugin for browser will be carrying on, though I will include the html document that links to the swf file anyway (for those who must run the Universal version). Scout out the internet and I'm sure you will eventually find a standalone Flash Player that will work to run this software.
The .fla file is only for those who need to take a look at my code.
The 'X' number field box is located in the upper-left. Simply type any number in this box and click the dark red 'compute X' button to draw a star with that number of sides. Pressing the up or down arrow keys will automatically increment X and begin the redraw. Pressing enter will start the redraw without adjusting 'X'.
As I was programming I needed a way to display all of the lines with uniform color in order to more easily count the incidences of line intersections and overlapping triangles, mentioned in the 'Equations' display. The Color Adjust Slider is useful in this mode, and will determine the final color that is applied uniformly (provided you leave the 'C' automation off). As soon as you finalize the color, you can do a final redraw in order to see the entire geometry in one uniform color. Though I have now included a greyscale mode color palette, it does take a little patience to get the star to draw specific white or black lines, or to find any given color you may desire. To find bright colors, I recommend turning up the opacity and using the rainbow 'a' color mode.
With stars over 60 in 'X' value, we no longer see the lines, we only see the occasional empty space where no lines are drawn. This makes it look like a circular gothic church window, but if the lines are all colored it becomes harder to notice the negative space.
First of all, the 'opacity' is for adjusting the intensity of the colors, but it is also the inverse of the transparency. We use the alpha channel to do this. If your aim is to print out a star, you may want to draw it using more intense colors, so in that case you may want to increase opacity to maximum. Yet if you want to more clearly see the places where lines overlap, having a low opacity (and thicker line thickness) will reveal this aspect. Also it is of note that when a background is activated it uses the value of this slider so that we can also control the background's intensity. Behind all the backgrounds is a black layer, thus by decreasing opacity the backgrounds simply appear more dim. For a bright background color, increase the opacity before activating a background ("o" key).
Its fun to play with the 'opacity' or any of the other sliders to influence the drawing.
The 'A' button beneath the Opacity Slider is used to automatically modulate opacity at a slow speed by default. Essentially for artistic purposes, this is used to adjust opacity dynamically during the drawing process. Grabbing the slider and lightly throwing the controller when this 'A' mode is on will set a controller oscillation velocity. The timing and velocity of the oscillation of the 'A' automation of the 'Opacity Slider' will greatly influence the final result. Simultaneously, adjusting the 'Draw speed' will also influence the final result when using this feature automation.
The color source in this software are routed from a collection of six images that are treated as color palettes, the new one is for the retro greyscale, including areas of black and white. The color adjustment slider changes the X and Y displacement of where colors are sampled from the currently selected color palette image. Colors are only displayed via the star's drawing process, so it can be a challenge to find any specific color. In the default symmetrical mode, each progressive layer of the star will sample a new color, but if you turn off the 'Preserve Symmetry' switch, it will repeatedly sample a new color for each new line, making it easier to see which colors have been selected by the 'Color Adjust' slider. In 'Monochrome' mode (the checkbox above the sliders) this will draw just one color when the slider is stopped, any color from one of the six hidden images. Once colors have been adjusted to your preference, you can redraw the star again by pressing 'enter'. It's fun to play with the color adjustment slider as the star is being drawn in order to get customized results.
The 'C' button right below the Color Adjust slider will gradually change the color offset during the drawing. When this mode is on, the velocity of the oscillation is set by the user simply by grabbing and throwing the controller in either direction. Default velocity is a very slow adjustment. Because the 'Draw speed' can also be adjusted, the possibilities of how we access the color pallets increase. Also, paradoxically, even in 'Monochrome' mode, if 'C' automation is on, the colors will still be changing as the star draws, because the adjustment is constantly moving in this mode.
The thickness of lines drawn can be adjusted with this slider in real time during a star drawing process. Being able to adjust the thickness of the drawn lines as the geometry is drawn will allow many different results. When the automation 'T' is on, gradually changing thickness at a default slow rate, the results will be diverse yet nonrandom; gradually or quickly changing line thickness. The velocity of change of this parameter is specified by grabbing and throwing the green fader handle either up or down. When 'T' slider automation is on, the 'Draw speed' slider will also influence the way this paramater ends up being applied.
All of these automations can now be adjusted to any velocity and continue oscillating simultaneously while the star is drawn, producing highly artistic results, which are different every time.
These are the six buttons directly beneath the 'A' 'C' & 'T' automation buttons. They directly interface with the six color pallets and determine which set of colors (or grays) will be used. The color pallet switching can also be easily done with the 'a', 's', 'd', 'f', 'g' & 'h' keys. Color pallets can be switched during the realtime drawing of the star, and will influence the final product. If one prefers a more chaotic result, the user can switch off 'Preserve Symmetry' and then the colors can be instantaneously changed with each new line, not waiting until the next layer of the star to apply their color change.
This is the button with the flat plane and an arrow either from above, or from below. This button is located directly beneath the Color Selection buttons. Fairly cryptic I suppose unless you happen to be reading this. The flat plane represents the star drawing from the horizontal perspective, looking at the edge of the page. Each new line will be drawn either 'on top' of all the previously drawn lines or it will be drawn 'underneath' all the previous lines, depending on this button. This feature as well can be switched in real time during star drawing. I prefer to use this feature to layer the new lines under all the others, making the lines at the periphery of the star on the top, and the final core lines of the star going beneath the rest of the lines. Again 'Preserve Symmetry' also applies to this button if activated, meaning that by default any change in layering behavior won't usually start until the drawing of the next core layer of the star.
Several years ago when I first began tinkering with star-drawing software, I took up a study of the counting of the aspects of these stars. Finding the total number of lines drawn to make one of these stars uses an equation called the Lazy Courier's equation. Another equation gathers the total number of possible triangles contained in the star. Another equation gathers the total number of angles formed by intersection of lines in the geometry, and yet another can predict the number of points formed by line intersections, all of these based on the parameter of 'X' value, the total number of sides of the shape.
There are some interesting caveats to these equations. If two lines intersect, they form one point. But if three lines intersect, they form three points overlapping. And if four lines intersect, they will form six points that precisely overlap. The equation determining the number of points formed as a function of the number of intersecting lines is given just above the equation that then determines the total number of points formed in the shape.
Again, with the numbers of possible angles formed by the intersection of two lines, we have four. But with the number of possible angles formed by the intersection of three lines, we the have twelve angles. With the precise intersection of four lines, we have 24 possible angles. This sub equation is included just above the equation giving the sum total of angles in the geometry as a function of 'X'.
If 'X' is whole, the results of these equations will also be a whole number, with the exception of the two sided object (line) and the three sided object (which my equation suggests contains zero triangles).
Adding the geometry summarization algebra to this software means it is well-suited to the realm of education. I'm happy to provide a healthy distraction from the current global emergency, no matter which age group.
This simple checkbox determines the direction that the lines are applied from the start, either clockwise or counterclockwise (the default setting). I don't know why I bothered to include this feature but maybe in Australia it will matter?
Found on the right side of the window, this is perhaps the most important feature because it determines how much your computer will be tasked in the draw process. If you set it to the maximum (top) of the fader, you will see the star drawing as fast as possible. The only way we could draw it faster than that is to use a 'for' loop, but then we wouldn't get to see or play around with the drawing process as the meta-logic allows. If you try this with a high 'X' value such as 60 or 99, you may find that it begins heating up your processor and your computer's cooling fan will turn on. If you don't like that, just adjust the 'Draw speed' to a lower value, and though it may require more patience to see the final result, it will then be less of a serious task for your processor.
Choosing the Draw speed makes a critical difference when using slider automation ('A', 'C', and 'T') that control the lines as they draw.
This feature, found on the right side, can be helpful to your equipment if you are somehow accidentally overloading it. Whatever is going on, being it the drawing of the star, or the rotation of the star, this pause button will pause all of it instantly and allow you to un-pause it and resume draw or spin (or both) with no issue.
This checkbox is found in the lower right of the interface. During the drawing process, if the 'Preserve Symmetry' mode is on, the opacity, color adjustment and line thickness will only be updated once the next core layer of the star is drawn. If this mode is deactivated, these parameters are gathered and applied instantly for each new line.
For people who don't know what symmetry is or what symmetry breaking is, this checkbox can provide a short visual education.
As each line is drawn it is counted in this field in the lower right. The final total of lines drawn should match that predicted by the algebra given in Equation Mode.
There is one context in which this lines drawn count is essential. Say you are using the 'Monochrome' mode with the 'h' greyscale color pallete and you have selected either jet black or a very dark grey. It would then be impossible to really see what is being drawn until a background is activated via 'o' key and (<, >) ',' & '.' keys. Therefore when drawing a black star on the initial black background, it can help to note the total of lines drawn.
This feature is located in the lower right, but is operated on with keyboard controls. A black background is the default (background number 1). If you know the number of your background you can type it in and then click the grey button, or just press 'o' key to quickly activate the background.
Once a background is selected, the lowercase '<' and '>' keys (',' and '.') allow you to navigate the array of 18 pre-programmed radial gradient backgrounds. Depending on the colors you've selected for your star, any given background can be tested to find the most pleasing combo.
Or, if you're not feeling all bright and colorful, you can even draw a greyscale star and select one of the greyscale backgrounds. Also a blank white background has been included as well to make sure the output is printer-friendly (uses less ink).
The background intensity is adjusted via the 'Opacity' slider. To make a background dim, decrease the opacity. To make a background brighter, increase the opacity. New intensity is visible as soon as we reactivate the background using the 'o' key.
Redraw of the star object is triggered through the enter key. Using the 'Up' or 'Down' arrow keys will increment 'X' by plus or minus one and then redraw.
The space bar can be pressed to activate and deactivate object rotation. Object can also be rotated while it is being drawn. 'Right' and 'Left' arrow keys adjust the torque applied to the object, allowing it to be gradually rotated in either direction. Rotation activates and deactivates smoothly. If your object is based on a high 'X' value it may significantly task the processor to spin it.
The 'a', 's', 'd', 'f', 'g', and 'h' buttons will switch between the six color sets, which is useful during drawing when the interface is hidden.
The 'p' button instantly pauses the drawing and/or the spin of the object if it is being spun. Pressing it again will resume.
After pressing the 'o' key to hide the interface and activate the background, the '<' and '>' keys (lowercase, the ',' and '.' keys) will navigate incrementally through the 18 different possible backgrounds. Intensity ob backgrounds is determined by opacity slider in the interface.
The Flash player includes a contextual menu, activated by holding the option key (on a mac) and clicking anywhere on the screen. Same can be activated by right-clicking anywhere on a PC. This menu contains zoom-in, zoom-out and print options. A white background is included in the backgrounds to help save ink.
When spinning the object, the mind will become accustomed to seeing it spinning. When we stop the object from spinning, after it gradually stops, frequently one may see it begin spinning backwards for a few seconds, but it doesn't actually spin backwards after it stops. I showed this to my father, and he noticed the same optical illusion. It turns out that the 'spin object' feature of this program (triggered by the space bar) can trigger a brief hallucination. It's non harmful but I guess you may be disoriented or distracted slightly by this hallucination, so be careful.
This program is actually very special because it demonstrates an application of algebra and introduces one to thinking based on variables, which are conveniently whole numbers (again). By watching the drawing process of the star it not only gives one a feeling of logic and order, it provides intuition into the numerical factors (even divisors) of your chosen X value. It gives each number an animated feeling, and can graphically show the difference between an even number and an odd number, or even a prime number.
The 'Preserve Symmetry' checkbox can give us a sense of what symmetry and symmetry breaking could mean. And while providing all of this for us, it hopefully can also be fun at the same time.
Happy holidays,
_Thomas L. Chenhall