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March 19th, 2010, 01:36 PM   #1
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So, I drew this, now I can't figure it out

Was screwing around with CAD, and drew this pattern, using just pentagons of the same size.

As you can imagine, it's getting a bit tedious to continue increasing it's size, and now I'm trying to write a macro to do it for me automatically. After two days now of pulling my hair out trying to write the macro, I'm at a loss.

I've added some color to the images to show what I want to do with it when it's done, but was wondering if anyone can give feedback, or perhaps point to a name/formula for achieving this pattern, as I'm sure it's been discovered before, but I can't seem to find it.

Click a Thumbnail to enlarge

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April 1st, 2010, 12:10 PM   #2
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Re: So, I drew this, now I can't figure it out

Hello pletch,

Maybe a bit late, but maybe I can help you.
It seems that one can calculate some angles here. For a start: The pentagon you used is made of sides with angles of 108 degrees. May be found by \frac{180(a-2)}{a} with a is number of angles. Here: 5.
Furtheron the white star. The "spike" of the white star has an angle of 180-2(180-10=180-2*72=36 degrees. Now we can calculate the angles of the diamondsuitschape. The angles around a point are added 360 degrees. The diamondsuitschape lies with 2 angles of a pentagon and 1 "spike" of a star. We've seen: angle of a pentagon is 108 degrees, a spike is 36 degrees. 360-2*108-36=108. Notice that opposite angles are equal in the diamondsuitshape. given a fourangle(is that the correct word?) is 360 degrees, and 2 angles are 108 degrees, the other 2 will be =72 degrees. Can you now calculate the angles of the purple shape?

I'm not familiar with macro's to do it automatically, maybe some-one else can help you on that one?
Good luck

Hoempa
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April 2nd, 2010, 03:38 AM   #3
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Re: So, I drew this, now I can't figure it out

Thank you Hoempa,

Your reply really got me thinking about it a bit differently.

So I ended up setting up the macro this way (note: this is far from the optimal method, I'm sure, but so far its the only way I've found, and for artistic purposes, it's close enough):

Made an object consisting of 5 polygons objects all pentagons and grouped them together as a single object. (for some reason this is a bit more difficult to macro than to simply create it as an object)



With each group of pentagons inscribed in a 1" circle, I found the distance from center to center of the circles to be 1.84927588 (why I have no idea, but for artistic purposes, it works)




then took 360 / 5 = 72

so placed 5 objects at 0, 72, 144, 216, and 288 degrees with an offset of 1.84927588" from the first point (macro lets you pick a point by direction and offset)
each of the 5 objects was inserted with a rotation of 180 degrees to flip them upside down from the first one.
as they were inserted, each was named with it's angle and rotation (a or b for 0 or 180 degrees) so the objects were named 0b, 72b, 144b, etc.



Some other technical thing, they are colored now in the images to show that they are locked, so that the macro does not try to reread ones that it's already copied.

Then the macro reads the name of each, and copies it out it's angle + 36 degrees at the same offset of 1.84927588" as well as it's angle - 36 degrees at the offset. (note: the angle and offset are from the center of the object from which the name was read)

Each is inserted at a rotation of 0 to be upside down from the previous row.

again each new object is saved with the name of it's angle and an indicator of it's rotation, so these are called -36a, 36a, 36a, 108a, 180a, etc. (thankfully duplicating names does not matter)



same steps repeated again (colored objects are locked so that they don't get read and copied again (also note at this point there are duplicate objects placed over each other using this method)....



Unfortunately, now I need to find a way to make it do this, which means not duplicating the pieces in the middle of each angle :/ ugh, so far so good, but this next step is giving me problems, and to make this scale out infinitely does not seem so doable yet.





So far so good, but still some work left to do on it.

And here are a couple interesting patterns that came up from failed attempts at creating the macro the first few times.





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April 2nd, 2010, 03:59 AM   #4
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Re: So, I drew this, now I can't figure it out

Hey,

You're welcome.
You calculated the distance between the centres of circels, maybe an exact number can help you. Are you familiar with sinus and tangens?
The distance from center to center can be calculated by adding distance from centre to spike, distance through the diamondsuitshape, and again the distance from spike to centre.
Assumed the sides of the pentagons are 1 Gives me in degrees: tan(54)+tan(72)+2sin(54). That is not the value you've found. I hope you were correct.

Hoempa
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April 2nd, 2010, 04:14 AM   #5
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Re: So, I drew this, now I can't figure it out

So it finally clicked...

Even though the groups of 5 pentagons is what I worked with to create it originally by hand, in order to macro it properly, I need to use this group



and the simple copy offset in 10 directions 5 at 1 starting distance, and the other 5 at a different starting distance.

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April 2nd, 2010, 04:19 AM   #6
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Re: So, I drew this, now I can't figure it out

Hey,

You have found a nice solution there!
Good luck,

Hoempa
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April 2nd, 2010, 12:43 PM   #7
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Re: So, I drew this, now I can't figure it out

Thank you for your help, it really got me to look at it a bit differently, it's funny how you can do something one way by hand, and in order to easily reproduce it with the computer requires a completely different approach.

Hard to believe there are so many different patterns that can be done with 1 shape creating so many others.
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April 2nd, 2010, 10:39 PM   #8
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Re: So, I drew this, now I can't figure it out

Have you ever tried this?

-Draw a square.
-All side of the square are sides of a triangle with all equal sizes (I don't know the words on that one), draw the 4 triangles in the square.

Suggestion: try figures with more, for instance 6 angles, all same-size and same-angled (for 6 angles, all angles will be 120 degrees).
Easy pattern, but I liked it.

Hoempa
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April 5th, 2010, 01:25 AM   #9
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Re: So, I drew this, now I can't figure it out

I really like the Amman Chair tile pattern, I frequently use it for borders around the images I do.



Usually I do not do repeating patterns as such, and find that working with odd numbers yield the best results

Here are some samples of the things I typically draw:

3



5



777 (Still a work in progress)

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