A Fractal Representation of Pi… In a Crop Circle

The 150 metre diameter crop circle in Wiltshire, UK (© Apex)

In the south of the UK, crop circles are a common event. These strange, flattened patterns appear suddenly and without explanation in farmland throughout the county of Wiltshire. Skeptics will argue that these patterns have been made by pranksters or by enthusiasts wanting to create large-scale crop graffiti. Others will argue it is an attempt by extraterrestrial beings to communicate with us by stamping their presence into a field. I’m keeping an open mind as to the source of these features, neither agreeing nor disagreeing with either “skeptic” or “believer”. And this is the reason why. The UK’s most complex crop circle appeared in a field earlier this month, and it took an astrophysicist to decipher what it meant…

I usually don’t cover stories like this on astroengine, but I thought this was pretty captivating. A crop circle, measuring 150 metres in diameter appeared in a field last month, and at first no one knew what it meant, and filed it under “C” for “Cool Looking Circle.” That was until a retired astrophysicist saw the aerial photograph above the Wiltshire countryside near the village of Wroughton. Mike Reed realised that far from being an interesting pattern, it was in fact a graphical representation of the mathematical symbol π (Greek letter pi). Complex crop circles have appeared before featuring fractal patterns, but this one is a geometric shape that accurately depicts the first ten digits of π.

π = 3.141592653

Reed managed to understand what was being communicated and drew up his graphical representation of π to 10 digits. Although it may not appear obvious at first, the crop circle above has been designed in the following way:

A graphical representation of Pi (© Mike Reed)

But how does it work? If you cut the crop circle into 10 pieces, the pattern becomes obvious. You have to start in the middle, at “1” in the diagram to the left, and work clockwise. It is important to take note of the “steps” as the spiralling black line progresses outward. The first number with a step immediately after is the number “3”, we make a note of this number. As in the crop circle in Wiltshire, there is a small circle embedded in the step noted as “1”, this is a decimal point. Progressing beyond the first step, we immediately hit a second step, so this means we make a note of the number “1” (giving us 3.1). Spiralling outward we hit a third step at the number “4”, we make a note of this number (giving us 3.14). As we continue, another step at “1” (3.141), and then at “5” (3.1415), “9” (3.14159) and “2” (3.141592). This pattern continues to the end of the spiral at the tenth and last digit. After this, there is a series of 3 circles denoting that π continues to infinity.

To be honest, I find this awesome. If this was created by a group of humans, it is a stunning achievement (although no one has come forward claiming responsibility). As for the other option (i.e. ET communication), I’m not so sure. However, as I was asked during the Paranormal Radio show with Captain Jack last week, “UFO’s, yes or no?”, I will have to respond with: Keep an open mind. Yes, I believe in extraterrestrial life, but as for them visiting Earth to communicate via crop circles seems a bit far fetched. Still, this is a nice little mystery…

Source: Daliy Mail

70 thoughts on “A Fractal Representation of Pi… In a Crop Circle”

  1. Yes, it took an astrophysicist to decipher it…in other words, someone like that did it! If humans could have done it, why jump to the alien explanation? Yes, we should have an open mind, but an open mind to evidence. Where is the evidence of ET? There is none. The computer I am typing with is a more stunning achievement than that crop circle. So who are the aliens that made my Gateway? Bill Gates is from the planet Sedna, I guess….

  2. I’m not saying that ET did, I’m just saying I can’t explain how it was done. It seems pretty obvious that if it took an astrophysicist to work out the solution, a human could have done it in the first place (could have been Reed himself!). But I’m on the fence with this one – if there is no clear explanation, I cannot conclude either way. The ET explanation is a fun one, in any case (as I touched on in the text) why would an advanced civilization fly tens of lightyears (assuming they are local) just to stamp around in our fields?

    I would like to see a circle for myself some day and see it first-hand….

    Cheers, Ian

  3. On the fence until I see something like this! Wow, those cirlces are awesome. I have no clue how these guys create these designs, thanks Zuckervati for the tip-off 😉

    Cheers, Ian

  4. Simplest explaination: people did it with boards and rope, then tipped someone off what it meant. If you see an alien’s hand in this you are just desperate to believe in shit like that. Lay off the X-files and drink plenty of orange juice.

  5. LOL, I get kicked in the balls for being “open minded” and I get kicked in the balls for being “a skeptic” – I can’t win!

    To be honest, before I wrote this article I was pretty clueless as to how these shapes could be made by stamping around in a field. That was why I was amazed after I did some reading to find just how complex a bunch of guys can make these circles.

    But, not all problems have a “simple” explanation, I think it’s healthy to investigate both sides of the coin before concluding (besides I never concluded it was aliens anyway!!).

    Too funny. Still, amazing patterns!

    So for my next article: “UFOs: That’s No Alien”, just so we’re clear 😉

    Cheers, Ian

  6. The circle only works in the decimal system…
    If it WAS E.T., and E.T. actually does know that the standard scientific system is the decimal system, then why not just write 3.14159… ?

  7. Yeah, it’s kind of unlikely that an alien race would use base 10 (if they’re so advanced they can travel between solar systems I bet they’d use base 12), and if they just made the circle in base 10 for us, then they obviously know our number system and they could have just as easily written “3.14159…”

    Also, I doubt aliens would use ellipses; if they did, again, they could have written pi out in decimal.

  8. really smart people aren’t going to go out in the night and make crop circles for mathmaticians to figure out. What would be the reward? Why not publish in a book and call it something else for that matter. Plus the equiptment involved to work in a field to make silly circles doesn’t lend it’s self to covert ops. It’s probably a flaky alien-savior cult. This fits the profile best in my opinion

  9. “I get kicked in the balls for being “open minded” and I get kicked in the balls for being “a skeptic” – I can’t win!”

    I wouldnt call thinking it might be aliens, or that there is a more complex solution being open-minded. Maybe you should of researched these? Openmindedness isnt a virtue (Like you make it sound) if it leads you to consider the possibility of such illogical thoughts.

    If its healthy to investiagte both sides of the coin….. Why didnt you investigate?

    Also, the phrase “it took an astrophysicist to decipher what it meant…” is very very misleading. You make it sound like it was only him how would of figured it out. You make it sound like other people tried to figure it out, also he isnt really an astrophysicist if he is retired, no more than I would be a policeman if I quit the force.

    If aliens are comuniacting with crop circles they are either retarded, by our standards, or have an awesome sense of humor.

  10. Having been involved in a group that made them in the US for a few years, I can assure you that the vast majority of these are confirmed to be of human origin. There have been websites appear and die over the years where people post pictures of their creations, and a great deal of “unexplained” crop circles were posted on these sites before they were discovered by the general public – no few are never discovered, since the good circle makers don’t damage the crop in the process, and they’ll stand back up in a few days if not found.

    It may have taken an mathematician to create the original diagram, but not to implement it as a crop circle. All you need is the picture, which existed far before the crop circle was created. The only interesting feature is the outline of standing crop around the three small circles. I’ve seen it done before, but not integrated into a larger feature so cleanly. It’s a shame the really good circle artists guard their methods so closely, I’d like to know how they made such a clean intersection on those.

    The complexity is nothing – the types of people involved in doing it are mostly math, engineering, and art students, all of which have the skills needed for more complex arrangements than this, and they’re always on the lookout for new ideas to outdo one another.

  11. Its not particularly complex anyhow. How difficult is it to divide a circle (360 degrees) into 10 portions of 36 degrees each and then use that to show any number of digits of pi?

    This is as amazing as waking up in the morning.

  12. Not to mention that there is no reason aliens would communicate in base 10. If anything is most universal, it would be a fraction in unary or something. And the fact that pi is based on Euclidean geometry, which is inherently flawed in a way that should be apparent to any advanced race. Utter nonsense.

  13. It’s wicked cool but I have three problems with it:
    1) Base ten system. Now, it’s not THAT unlikely because base ten isnt a number picked outta the blue, it’s how high we can count on our fingers before starting over. Five is a pretty reasonable amount of fingers. But still, it’s not likely.
    2) The decimals. Decimals are a weird system, it’s not as obvious as you’d think. It’s just one way of doing fractions and not a particularly good one either. The odds of aliens doing decimals the same way we do, even if they use a base ten system, are pretty low.
    3) Most damningly, the symbols. Come on, what are the chances aliens would use a period for the decimal point and “…” to mean something continues?

  14. The use of symbols and decimal are damningly human, but the pranksters certainly are a clever bunch. Pretty neat!

    Remember: Extraordinary claims require extraordinary evidence.

  15. but its wrong, its correct up until the last digit with the 3 circles indicating infinity. ie. 3.141592653 but the last number in the drawing is 4??? so whats up with that?

  16. I bet nun y’all thunk about why astrolophysissis makes crop circles. You’d think they’d have enough time with flying in space ‘n all.

  17. crop circles used as a map from outer space for incoming ships, but now those lands are flooded, so a mapping probe was sent up outside of the OZONE to guide the ships to either their underwater bases in the ocean or to create more havoc on all life on earth. i’ve asked the HUBBLE Telescope to contact NASA to have them push the prove out into outer space or destroy it, but NASA says their’s NO UFO”S, so why worry. we on earth have up to 20 years left to survive. GOODLUCK. http://www.inventube.com/ooojay/ AND http://www.socyberty.com/Activism/First-Step-for-the-Solution-to-Global-Warming.103109

  18. i hope the above comment is a joke (!!!). if not, please shave with Occam’s razor once daily…

    btw…there are UFOs (Unidentified Flying Objects)…

    as far as aliens that have visited earth…almost certainly not.

  19. Think about it. You’re trying to communicate with a planet you have never before made contact with… what better way to do it than encrypt a mathematical constant!

    If you had to set up a life in a foreign country, the last thing you’d think to do as a means of communication is a graph of a number.

  20. My theory..? People made it. The clue? It follows the common 10 digit counting system… 0,1,2,3,4,5,6,7,8,9…

    Perhaps this is a universal system, but I seriously doubt it. For all we may know, any other intelligent life may have developed a very differnt system for counting, such as the Octomatcs system here on earth, or even a system in which Pie can be calculated as a whole number.

    It is very artistic though.

  21. Let me tell you something about aliens. The universe is made up of all the same matter with all the same elements to form life. Any intelligent beings out there are most certainly very “human-like” at some point in evolution.

    So to suggest that aliens are some sort of super species is false. They are just other humans on other planets…for a comparisson to us, say in the year 4000. (By then we may even venture throughout the universe and find other human-like life to mess with.

    BTW those crop circles are done by some people with a cool hobbie. Not with boards and rope. They are using some other technology from this century probably.

  22. And on the whole counting debate…It’s different everywhere. The French don’t even have individual numbers all the way to 100 like the English do. To say 97 in French it’s (Quatre-veignt-dix-sept) Which in English means (Four-twenty-ten-seven) instead of ninety-seven.

  23. Ian, sorry, but you should know by now that whatever you say on the net is bound to have some idiot come and put you down for your beliefs/ideals, whatever. . . Just stick to what you believe in, and if something comes along that changes your mind, so be it. Just tell everyone else to bugger off and be yourself. And as for the crop circle, it’s possible for people to make it, but since there is a lack of evidence, you can’t prove anything beyond a reasonable doubt. So there you have it. You lack sufficient means to 100% prove or disprove, and thus, immagination and theory fill the blanks. . .

  24. I don’t think aliens would include a decimal point in the freaking crop circle. The decimal isn’t even consistently used here on Earth

  25. Ian O’Neill,
    Protip: You don’t need to defend you article with responses. It makes you look like a tool.

    It was well written and I enjoyed it very much. Of course people are going to debate the “UFO vs Human” factor, they’re a bunch of children. Most of them have no idea what Pi is.

  26. Very well written and interesting article. With regard to the question of who did it, one thing to keep in mind is, e.t.’s don’t necessarily use base 10. For all we know, we human beings are unique that we’ve decided to use 10 digits to do math.




  28. It’s not aliens… end of story.

    1: why travel trillions of miles to tell us something we already know?

    2: why make it so cryptic, it’s a number not a message.

    3: Are the aliens so dumb that they think we don’t know this already?

    4: IF it is aliens are they just trying to freak us out? IF so, then for what purpose?

    My money is on clever people with to much time on their hands….

    Still… it does look prettty 🙂

    1. The encription can be wrong.. Thease pepople have learned to encript thease puzzles with numbers, but not all can be revolved trough the same ideal. There is a complete different story behind the meaning of this.. And your 4 reasons are completely non sense. I believe that this indeed was not meant to be taken as Pie. This is completely something else, and by looking at this you really can't prove the pie ideal 100 percent by the different boxes each number is sepearated within.

      1. Let me add on to my hypothesis. One person trys to look at this, ” a well known individual in the field of crop circles.” By his observation i formulated that he hasn't observed this well enough and that their can be literally many meanings to this. What i think, but only my opinion is that it has to do with our solar system. All the circles are objects in our solar system. the middle object is our sun and since every planet in our solar system revolved around our sun we can say that the other three dots mean planets. The maze shown leading to the planets can be observed as many different things, but i think it means a path of destruction. leading from the sun every other moving object has been trough its destruction phase, and the planets are positioned at the end maybe hinting to us that destruction is our way. Their might be something we can do, and thgats why they have put the crop circle their to show us that the way we are going is leading us to destruction. But we can stil change. The last theee cirlces representing our different planets whos atmospheres have not been completely destroyed yet. One being our planet, another being mars, and another than im completely not aware of because im not into this study. Anyway to summarize my point, i want to point out to everyone that this cropcircle can be literally encripted into different meanings. In my opinion the middle circle is our sun and the final 3 circles positioned at the end of the maze are our planets that are approaching some sort of destruction. This is hinting to us that we need change. If anyone somewhat agrees with my ideal or wants to talk about it or question it feel free to email me at Pashayanhovik@yahoo.com

      2. Mars, Earth and Venus. Look at the sizes of each planet and compare them to the sizes in the crop circle. This is a photo about or solar system!… Venus and mars might be connectged with out world

      3. Or all three planets are going to colide. :}}} anyway the mewaning tingles withing thease lines.. nothing to do with pie!!!

  29. I kind of agree, the cryptic nature of the circle makes it far far more likely to be humans showing off than aliens communicating. If aliens were smart enough to invent working FTL travel they wouldn’t have a problem understanding and translating our mathematical system and could very easily just write. “3.142 etc. We’re aliens lolz, wanna cyber?”

  30. Uhm, the base ten numbering system, plus the use of a decimal to denote fractions of a whole, plus the use of ellipses to denote continuance, plus, you know, there are less ambiguous ways to let everyone know you’re here if you’re an interstellar alien makes me think it could just maybe be the work some humans who understand basic math and how to squash grass. Maybe.

  31. Any interpretation of that silly diagram is possible. Put appropriate numbers in the sectors, you might even get the population of earth…

    I guess you guys believe the “secret messages” predicting the future in bible too?

  32. You humans are so smart, you already knew about Pi!
    Sorry about that, the problem is everytime we left something you didn’t know, you did not understand…
    And you have answers for everything, I see… You are amazing!
    We are sorry about the misunderstanding, our PR department will research better in how we could communicate with you.

    P.S. I know skepticals are going to say I’m not alien, because I speak english and I know how to use a computer, browse internet and so…
    all I have to say is: We DO study, you morons!

  33. Ian how would you like to explain the 25 minute video “kill shot” by Ed Dames. The solar flares are real and if an object can come close enough to disrupt the magnetic field even temporally. Ed dame using remote influencing has predicted world economic collapse, a global pandemic and the Kill Shot. The issue is you are trying to play both sides of the “cool crop circle” instead of helping to prepare folks for the hard times ahead. Also ET are real just look at the many many other complicated designs out there. The crop circles are explained in the video.


  34. It really amuses me that right after the first number 3 theres a dot and that the 3 circles at the end mean ” …continues to infinity”. So I guess ET's would also use dots as puntuation marks. A single dot for decimals and 3 dots for ellipsis.Cranks me every time. Also… I can see the design was very conveniently placed over a dirt road. Great place to park your spaceship or truck and leave no evident marks… great idea!I like the design though. The “Cool Looking Circle” was spot on.

  35. The fact that it was an astrophysicist that first deciphered it doesn't mean that the intellect of the creator of the object would have to be that high (though obviously it wouldn't have been a moron).

  36. OK. Just plain and simple: They are man made.Any extra terrestrial life smart enough to get here wouldn't be stupid enough to encode messages in fields. Fields are not a good way to record data and they would be smart enough to know this. They are not only inefficient but don't keep their memory for long. They would be smart enough to use paper or electromagnetic waves AKA radio signals to communicate.So unless you propose aliens dumber than us flew all the way here to leave impressions on our wheat fields that have no relevance or purpose it is man made.

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