Crop Circle Project

[fedetony]

Back in December 2019 I started a project for myself in the search of something.. I could not define it properly, is a knowledge hidden within art, beauty, patterns, proportion, math.... I set myself to analyze crop circles geometrically and using only simple concepts of math. I studied the way they were constructed and then I followed to reproduce them only using a compass and a ruler, after the drawing base was done I proceed to color them with some some ink.
I found amazing things within each drawing, my aim is not to bore you to death with the complexity of it, but for you to see the beauty within some of these constructions.
C &C are always welcome. If you have question please do not hesitate to ask. I'm going to post in this thread my work hopefully I'll have enough time to show you the mathematical construction. The ink used is from technical drawing pens Rotring, and after a couple of drawings I decided to keep the construction markings. They cannot be seen when I scan the image but a side picture of the drawing will show them.

1) 03.06.2019 Littleton Hampshire Long Wood

This was my first one, I did it too small ..

2) 28.07.2019 Barton Stancey Nr Andover Hampshire

Made some mistakes so I started over

 

[fedetony]

3) 20.07.2019 Westbury White Horse Whiltshire

4) 23.07.2019 Pepperbox Hill Windwistle Lane Salisbury

5) 26.05.2018 Buckland Down Cerne Abbas

 

[fedetony]

6) 08.05.2018 West Knoyle Whiltshire

7) 09.06.2018 Hackpen Hill at Broad Hinton

8) 06.2018 Keyslay Down , Whiltshire

 

[fedetony]

9) 23.10.2019 Rodfield Lane Hampshire

10) 11.06.2019 Belmore Lane

11) Unreported??

 

[Iain]

These are a wonderful series. I like Pepperbox Hill in particular. The TD ink has them looking like prints. The side view of Hackpen Hill (wonderful names!) has an interesting surface, as if coated with oil stick. These remind me of a couple of my ink drawings.

 

[fedetony]

12) 21.06.2019 Solstice- Sparticles wood - Surrey

13) 01.07.2019 Danebury Hillfort, Middle Hallop Hampshire

14) 08.07.2019 Farley Mount Hampshire

 

[fedetony]

15) 03.07.2019 Yanbury Castle

16) 26.07.2019 Extinction Rebelion

17) 22.05.2019 Norridge Wood Nr. Warminister

This one I left it incomplete to show the construction

 

[fedetony]

18) 03.06.2019 Long Wood Littleton Hampshire

19) 11.08.2019 Preston Candover Hampshire

20) 04.06.2018 Ackling Dyke Sixpenny Handley Dorset

 

[fedetony]

This two in this post have something very special. They are constructed with only prime numbers until 100.
21) 20.08.2019 Etchilhampton Hill Devizes

22) 28.07.2019 Clear Wood Nr. Cley Hill Warminister

Well, there is one more is in my avatar icon...
Hope you enjoyed an overview of my crop circle project and the beauty of math...
Love

 

[fedetony]

Thank you Lain for your love reactions ...

 

[Enyaw]

The beauty of geometry. That must have been enormous coloring the shapes. They remind me of mandalas in black and white. Great stuff.

 

[ntl]

Oh my...
The originals are beautiful and mysterious.
Your renditions are wonderful.

 

[fedetony]

Thanks for the kind words ntl and Enyaw .
Yes it was quite difficult because the pens are really thin. and I had to be really careful not to exceed the lines. Also some are colored in the same pattern directions as the crops were lay in the reference images...(See # 19 for example)

 

[Terri]

These are beautiful individually, taken in a group like this they are incredible! I love the stark black & white, and the geometric shapes are beautiful in their simplicity. Absolutely wonderful work! Hats off to your care and patience and attention to detail.

 

[snoball]

These are every one absolutely beautiful!!

 

[laika]

Wow! I can imagine these as cool tattoos! Most impressive, fedetony!
Have you considered a brush for some of the inking?

 

[stlukesguild]

I set myself to analyze crop circles geometrically and using only simple concepts of math. I studied the way they were constructed and then I followed to reproduce them only using a compass and a ruler...

I'm fascinated with geometric designs, patterns, and tessellations myself... although my own influences come more from Islamic Art. While some of the Islamic designs can be incredibly complex, most were constructed using nothing more than a ruler, compass, string, and templates.

 

[joe1It]

wonderful job

 

[fedetony]

Wow! I can imagine these as cool tattoos! Most impressive, fedetony!
Have you considered a brush for some of the inking?

I did not try. I think it would make it easier for big areas, but also high risk in missing the lines... anyway I made these while I was in a trip so I had limited supplies with me.
@stlukesguild, yes islamic art is really elaborate in patterns, it is impressive when found in architecture.
Thank you Terri Laika stlukesguild and joe1lt for the comments .

 

[fedetony]

All of them had a mathematical study behind. I'll just give you the 22 as example, since I've documented it because I was really surprised it uses prime numbers. I thought it would be interesting to you how I achieved to get them reproduced. For it I normally develop it in a CAD tool called fusion360 using an aerial image as base and then check all the mathematical relations. Not as numbers but as tangents or concentric or intersected...

The previous images is what you obtain when you extrude the construction areas, but
check the construction required to build the crop circle:

I know it looks chaotic... They are all the prime numbers until 100 connected forming the figure. In the left I have the prime numbers that were not used in the construction. Here are the numbers:

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151

Here some images that bring some clarity:

Positions and diameters of all the circles are build using only the prime numbers. They are all connected by being Concentric and/or tangent circles forming the figure you see.