Friday, December 5, 2008

340 cipher solution

This is what I came up with:


"I will make this very clear. My one reason I am killing. If I don't kill I am likely too abandon my chance to collect my slaves for the afterlife. Even when I know you can't find me I am not safe walking if I am collect my slaves. When slaves you found saved dead in a car. He changed his mind and road form me. He walked by without hiding from me. Nothing was safe. He was hiding a knife. You even listened too my slave was calling for help."

This is a polyalphabetic substitution cipher, not a transposition cipher, which is why basic decryption programs that only have one letter substituted for a coded letter, are not compatible with this approach.

Another researcher and programmer pointed out that it has a 69%, one to one, accuracy rate. He said I could use this graphic he created to help illustrate the accuracy. In his email he explined.


I was playing around. I used your solution and made the assumption that each symbol would represent one letter in each quadrant. I used the first instance. Of course we know that Zodiac used multiple symbols to represent the same letter and also used symbols to represent multiple letters. By using the method I described, your solution proved 69% accurate.

Let me explain a little more in depth. If you go to the first quadrant (upper left), you will see that "R" occurs three times in the cipher. In your solution, "R" represents "I", "E", and "O" - in the first quadrant. In my test, it was only allowed to represent "I". I attached an image. When you look at the solution solved by quadrant and only using a single substitution method, it is impressive.

So far, this is by far the best solution I have seen. On an odd note, I found when you solve the entire cipher using your using the single substitution, it said something like, MAARYISASTINKINGWHORE," at the end. It had the name MIKE AVEY in the center. There is a military man from San Francisco named Mike Avey, but I haven't looked at it much because the rest of the cipher was gibberish using this method.


cipher 69%

The first two lines only have one wrong letter. When you consider the frequency of the other correct letters for the solution is very compelling. Also the accuracy for the first 5 lines is about 85%, the first 7 lines about 79%, the first half, 70% accurate.This seems very compelling and highly unlikely that another solution could be fabricated that would have the same level of accuracy.

Here is a photo of the cipher and solution. The circled letters are the ones that correspond to other shared letters in the other words.


I started by dividing the cipher into four equal quadrants then making a frequency distribution noting which quadrant for each letter.


This is the frequency distribution for each character:


Notice that some of the coded letters are clustered in quadrants, while empty in others.

I took the most unbalanced coded letters. For example if there were four hits in Q1 and none in Q4.


And when these were circled on the cipher they also clustered together. This was my original.


I then noticed that in two of the clusters in Q1 (top left quad) on line one and four shared two characters that were inverted. It didn't take me long to hone in on "MA" and "AM", which was the first clue. And from the other Zodiac letters we know he starts with "This is the Zodiac speaking" But of course he wouldn't use that, so "i will MAke this very clear", was a logical start. At first I didn't know if it was "I will make this very easy, or hard." But "clear" became the most likely word after working out the rest of the cipher.

This is the frequency distribution for the solution.




The backbone of this solution is the first half, first nine lines, then line 14&15, "changed his mind", line 16 , "Hiding from me", line 16,17,18,19 "From me..." "was hiding a knife you even listened too my slave."

Then the gaps between had some strong words, however these were several other variations. On line 12 "saved" is very strong as well as "slaves" before that on line 11, for the subject, but "end" was solid for "dead" and could have been "ending his life a slave." But this wasn't the Zodiac's style of writing. He was always very clear and direct and his sentence didn't trail off with something confusing. And out of that variation, all there was was "end" and the rest wasn't solid.

"Without" on line 15 also had a variation with the same corresponding characters, but "hiding from." on the next line was still the verb. So, from entire sentence the "hiding from" was the only conclusive part, and the other word, "without" was the most probable considering the context. The other variation only had one extra letter, and didn't seem like Zodiac's style.

However, the other possible variations, would still use the same verb, and are very much in the same context and are not significant or indicate his identity. So, unless there is a variation with some compelling information, the minor ambiguous lines aren't enough to discredit this solution.

There were some very compelling occurrences that indicated most of this solution was an intentional method.

For example, on line four "Chance" and on line thirteen "Changed" both share the same characters for "HAN".

All of the "N" are the same character of the circle with the cross. The "^" has four "A", the "q" has 9 "L"'s, the backwards L had four "M's" backwards F has four N's.

The distribution in each quadrant is also noteworthy. The B has three S in Q4 and two A in Q1. which seems intentional that the letters of S and A were distributed evenly into separate quadrants. The "q" has five "L" in Q1.

What's more some of the more unusual combinations of coded letter and solution seem intentional. The solid triangle is an L in two places in Q1. The G is a C, V is a K, backwards L is an M in three places in Q1. Backwards F is an N in four places, one in each quad, and backwards F only occurs four times. The circle with a dot is an A all three times.

I didn't even notice any of these patterns and simply constructed the words that had the most corresponding similar letters.

I wonder if one of the victims had a knife that only the police know about?

The word "hiding a knife" had a strong hit.

There were some other variations with several of the other lines. For example, "car" didn't have any corresponding letters, and could have been "lot" or some other combination with the "In a car".

At fist I thought the last line was "stalling out hard" then I got "knife" and "ankle" on the 19th line, and thought the last line, line 20, could have been "falling out hard" as in a knife that was strapped to his ankle, and he was hiding sneaking away. However, "listened" seemed very strong. And once again "Slave" was just too strong in the end of the 19th line. I think he may have changed his mind in a few places.

I also think he was having schizophrenic episodes where his thinking was fragmented. There was a witness at the Stein cab killing. So, this does make sense. I also think he may have changed this to "calling out for help." It just seems like part of him wants to get caught and the other part is very deep into a compulsive disorder that he can't control.

Keep in mind that this cipher would have taken him a long time. It would have been a painstaking process to make it all work out to be neat and even. So that is why it may be slightly fragmented. Although, this solution in cleaner than the 408 solution that had a few extra letters here and there.

The spelling is also pretty good in this cipher. There was a "too" instead of "to", and the next "to" could have been an "at", as the only other solid "p" was a "t". I think he used the longer "too" to throw off the solution, but it is also possible it was a misspelling. Sometimes, people wonder why he spelled well in his ciphers or in some letters while not in others. He probably had a dictionary at home where he made this and his other quick notes were composed in a car. He didn't want to carry around any letters that could incriminate him and composed them on the spot and mailed them off. Most of them appear to be rushed like this. Some appear that he made most of it at home, then signed it right before mailing it. Regardless, I think people make too much out of his spelling or assume he could spell when he didn't unless he had a dictionary. Some words he probably intentionally misspelled to make it appear that he was intentionally misspelling words, but I don't' think his poor spelling was intended to prove he was unintelligent, as he didn't miss the chance to claim a superior intelligence and ridicule the authorities, and his spelling mistakes will help identify him.

Finally, the fact that there were such a high concentration of single coded letters in each quadrant, such as six "B" in Q4, five "q" in Q1, indicated that he substituted different letters for each coded character. If not there would have been very obvious words found a long time ago. There were a few places that had a slightly more accurate translation, but didn't fit the context as well, or didn't resonate the Zodiac's cadence and structure. He was pretty clear and straightforward.

Any suggestions, observations, or if you can find a more plausible variation using this approach, feel free to contribute!


4on4off said...

You said that you divided the cipher into four equal quadrants but with 17 columns how is that possible? Do you have a seperate key for each quadrant or one key that works throughout the text?

Thank you for your time.


John Cecil said...

There is a center line of text. Notice that I put any letter that fell into this center line off to the side between the two quadrants.

It makes no difference. I simply plotted out the frequency of the unsolved cipher text for each quadrant.

Someone else pointed out that this solution has a 69% accuracy for a single letter for letter substitution.

Anonymous said...

I think your idea is closer than any i've seen. Note that the "+" falls in the middle of cipher and at both ends of the row with that "+" are two "-". The large zodiac symbol at the very bottom is also centered on the column with the plus. I also think the paradice/slaves cross in the Halloween card was a clue for this cipher.

John Cecil said...

yes, I also thought the Halloween card had the same concept of dividing things into a quadrant. You can see that I circled the tenth line as the center dividing line, even though there are 20 lines total. The last line, line 20, is also kind of spelled phonetically "Zodiac" as many people have noticed, so this may have just been his signature, which would make the 10th line the center. I think this was his intentions to help mix things more, and the 20th line has a double purpose as it works in the cipher and spelled "Zodiac" has his signature right after his trademark circle with the cross. It fits his pattern or having a hidden meaning with side clues, with a slight deviation.

It seems he was aware of how his coded cipher would be distributed into each quadrant, the Halloween Card had the same concept, he gives the clue the 10th line is the center, and the 20th line has a dual purpose, as he uses "Zodak " right after his trademark, that he leaves on all his letters.

Smoku said...

so if its true zodiac said about that there was some unknown witness to some of the murders ? Sounds like "thou im killing its dangerous because recently when i was killing a possibly unarmed or harmless person someone other was walking by hiding a knife and despite that he didnt do nothing about it even when the victim was screaming for help" Is that whats hes talking about ? Does he think that hes trying to show that he has still a strong sense of morality or to show us that there arent "good sides" in this investigation ? Writing style sounds a little like he wouldnt care , it doesnt seem have the emotional subtext. Maybe he had a crusade toward the establishment thing coming to an end seeing that its even more immoral to not help a dying man rather than killing them ? He felt almost sorry for the victim ?

John Cecil said...

Smoku..interesting observations. A few other people emailed me with some very good insights and I wish they had posted them here.

I wasn't sure about the knife either and thought about what that meant. After the first four of five lines the part with the knife was the next part the translated. If you look at it, it says, "I was carrying a knife" but after sorting out the rest of the cipher, there were two letters and "He was carrying a knife" made since. Maybe the victim had a knife? Zodiac was saying nothing was safe, and this killing he almost got caught.

Although, I think the deeper meaning is interesting.

It didn't seem to care about the victim. I think you are on track about having something to prove to society. And, I having thought too much about "you heard my slave calling for help."

Somehow he knows there is a witness and this is a big deal to him. He is doing everything for attention, and seems for the first time to realize that he will be identified.

Mabye, "he passed by without stopping" was the cab driver passed by without stopping to give him a ride, and Zodiac found him or some other cab driver later walking or something?

There was a witness to the Stein cab killing.

Christopher said...

This is very compelling. I was working on this cipher and then found out that you had mostly solved it. I was beginning to use the same method as you. The first three sentences seem solid. Without looking at it closely, I think there's a chance that some of the phrases and fragments later in your translation may be a bit off but the general message is there. I do agree that some of his language was fragmented so maybe your solution is right on target. Congratulations!

On a side note, I would like to share something that I believe was never fully solved, the 408 cipher. Everyone was saying that the last line of characters were just "nulls." If you use a polyalphabetic method consistent with the "mispellings" in that cipher and use transposition, the last line should read "I will not give you my name because you will try to slow down or stop my collecting of slaves for my afterlife BEFORE I MEAT THE SFP" (my solution in caps)

This suggests that he did intend on actually meeting the San Francisco Police. If I recall correctly, he brags in another letter that he did in fact talk to a cop right after one of the killings but he was not suspected and actually told the cop he saw someone running the other way. This is the first public forum in which I have shared this information and I am unsure if it is a stretch. I don't know. What are your thoughts?

John Cecil said...

Christopher, thanks for your comments. I'll take a closer look at the end of the 408. I think you are on to something. He certainly had some resentment with the police and rarely missed an opportunity to taunt them. But at a first glance, the "BEFORE I" seems consistent. How solid was the translation? Could it be "before I die?"

I plan to take a closer look at the 408 when I have time.

Email me if you want,

MattSaxim said...


When I found this site at first I was I felt a bit upset I think it was caused by wanting to be the only one to crack it. then I went outside, sat and thought. Then I began to feel intrigued because of how this world works. how two minds can work so much alike!! all that work that I had put into solving this cipher and someone else on the other side of the country came up with the same exact method as I. its amazing not many have noticed the + that breaks the Cipher into 4 quadrants. what I came UP with is a little different, but extremely close than yours. I will e-mail you my work for you to take a look at. who knows maybe we can work some on some of this stuff together. I live in north cali So I can check out the sites by MT Diablo

at first I wish I hadn't come by this site, now I'm glad I did. I found a Like minded person.


Take care!

John Cecil said...

Hi Matt, thanks for expressing your thoughts and reactions. The solution might just be like minded people working together. That's great you also had the same approach of breaking it into four parts. I'll be glad to take a look at your approach and results. I've also made some more progress but hit a limit for the time and effort. That would be very fitting if someone from California solved this one or put this case on the right track. I'm kind of busy with work but would be interested in keeping an open mind and see what kind of progress can be made. Keep in touch!

Anonymous said...

This looks like data mining to me. Ingenious, but too ingenious. The zodiac killer was not that sofisticated when it comes to creating a cipher - he was quite ordinary in that respect. But like ordinary men he could spell better than 69%. Sorry, no cigar.

Anonymous said...

Nice job. I have another observation regarding the Halloween card where “paradice slaves” breaks it into the quadrants. I am not sure if this was asked already, but the quadrants in the card have “by fire”, “by gun”, “by knife”, “by rope”. Each quadrant in the cipher has the word “by” in it before solving it.

In your solution the word knife ends up in the same quadrant that the Halloween card has it in, and in the last quad you have “by” in the solution. Did you look to also get the other killing methods and the word “by” into their respective quadrants as part of the solution?

John Cecil said...

Hey Anon, I didn't notice that! Great observation. It took me a few minutes to understand your question. Off the top of my head I don't recall any of the other words from the Halloween card in the 340 cipher solution. I'll look over it again. I remember the word "knife" was strong and was one of the first words that was found. Thanks for posting!

Anonymous said...

Thanks. Post any results, would be interested if you found anything. This guy is that old Russian saying “It is a riddle wrapped in a mystery inside an enigma.” Two other things I noticed are:

Dann says he saw a name “Avey” in one solution. AveRy was the main reporter on this case and the one zodica mailed the Halloween card to almost a year after he sent the 340 cipher. It’s been noted zodiac was angry the first cipher was cracked so quickly. I think he may have been frustrated a year later when he figured it was too hard and would never be solved frustrating him even more so he created the card for Avery (though he spelled his name wrong on the card “Averly”). Anyway my point being Avey could be Avery if the “e” is really a “er” or if the “y” is really a “ry”. Not sure how that would influence the rest of Dann’s solution.

The second point being in the card all the word “by”’s are horizontally penned, except for the one in the knife quadrant. That one is vertical. Knowing how tricky he considered himself I can’t believe that is by chance. I am wondering if some of the cipher goes from top to bottom instead of the traditional left to right? This could be just a coincidence, but I don’t think so given his frustration at not being solved.

Thanks again.

John Cecil said...

As Dann said it was just a side note he mentioned when he applied a straight forward letter for letter substitution from the first quadrant to each. I asked him if it was ok to use his observation and graph he made that my solution was about 69% accurate and he said it was fine so I simply included his email to me that included his side note about Avry.

Anyway, I didn't consider that the Halloween Card was sent almost a year after the 340. It is plausible that there is some other insight with the Halloween Card, and the fact he used "by" vertically in the fourth quadrant of the Card suggest that he may have done that in the cipher as well.

As your quote suggest, it is probably some simple twist, an enigma within a riddle, and he probably was frustrated for whatever reason that the FBI didn't solve it.

The 340 was probably something that evolved and he decided to make changes and add more twist and turns.

I think if more real code breakers were aware of this solution someone would figure out the complete solution.

I'll take another look at it myself and see if I can find anything with some of your ideas.

I think you are taking the right approach and have an accurate assessment of the complexity.

themcnx said...

Least likely, so many grammer mistakes. The Zodiac is too smart to create that much mistakes

Anonymous said...

i believe this to be wrong, in the 3 part cipher he did not change the key half way through... i doubt he changed this one, and i bet this one is just his way of getting his rocks off knowing the police and public would try to solve this one while knowing there is no solution to it.

Anonymous said...

I have found the reference to all the texts. The 340 code references, pretty well, a hate for prostitues. For those who wish to figure out how. A starter for thous who doubt is the "My name is ____" letter. Easy enough if you want to know. A little help would be that "ALL WANT TO KNOW MY NAME".

Cevolinga said...

Just a thought... has anyone every looked at Gary Ridgeway (Green River Killer) as a possible suspect for Zodiac? I've just been doing a little checking and supposedly Ridgeway attacked his first victim in 1966-67 in Green River. This would have been about the same time as the Zodiac was running rampant through SF. Just a thought. Sometimes it takes someone to ask the right question.

Anonymous said...

This has been excellent reading! Thank you for being as obsessed and much smarter than myself in all things ZODIAC.

Smithy said...

You're surely not serious?

TravisD. said...

Wow!Well finally I can stop banging My head.Your solution I believe is right on for in fact the the writing it states is a formitable match to His previous letters.It also states that He kills a Man who pulled a knife on Him.Has anyone ever found Police reports of another Man being killed by knife who had a Knife Himself?

I was basing the cipher on scripted ancient texts' and languages because so many of the symbols He uses are use in multiple ancient texts.,Trav.

TravisD. said...

Hello to Anonymous!I was reading Your comment about the Zodiac not being sophisticated enough to be able to pull off this cipher,which got Me thinking The authorities and FBI proved to a good percent the Zodiac was ex-Military.Who knows,He could have been a cryptologist or someone who worked secretly with certain codes in the Military.

Reading His letters and noticing how well He could spell certain difficult words in the,I doubt if He mispelled on accident.You never know,the mispelled letters in all His sent letters might ad up to something He planned out.He was smart,smart Pscychopath,but smart all together.Man,He left the world wondering.,Trav.

Anonymous said...

You said there were extra letters rite. Well maybe they were meant to be there. Maybe the extra letters are meant for a differennt cipher like a supstitutional cipher.

Anonymous said...

Zodiac 340 cipher solved. Name revealed : Daniel Sentino!! Read :
Zodiac 340 cipher solved

Anonymous said...

I was just googling a bit on the zodiac, and came across this site.

I read something about Lyndon Lafferty has found the identity of the zodiac, but won't give his name to the public. He "claims that the killer was motivated by jealousy because his wife as having an affair with a senior judge"

Another site claims Lafferty is talking about "William Joseph Grant" who was married to "Marion M. Grant"

Having read this, i found the part of "MAARYISASTINKINGWHORE" quite intruiging.

doranchak said...

There are many problems with Lafferty's claims. Here's an analysis:

Holger W said...

hey! i'm from germany so please excuse my bad english.
i think it's the right solution, but these are just my thoughts. i was very impressed by your method. it's not an unusual way to solve a code like this and that assured me that it is the right solution.
but i don't believe that this cipher wasn't solved till this day you cracked it. i think the sfpd or the fbi solved it in a couple of days maybe weeks. they didn't want zodiac to know about, perhaps they wanted to provoke him in this way so that he gives them more details about himself, his writing or what else. maybe the sfpd just didn't want to give him the attention that he was lusting for.

John Cecil said...

Holger, that's interesting that this is a common approach to solve other solutions. I think that's what a lot of people trying to solve this are missing. I wan't able to verify any of it, though, but it is very encouraging that others recognize the identical style as the Zodiac. Even in WWII code breakers could predict someone's style once they knew this much about the person making the code. What were they trying to say? Etc, and in this way search for words that make sense. IN short the Zodic is predictable.

I always thought someone from Europe might solve this case. I would suggest reading the John Nash biography by Sylvia Nasar who is also from Germany. If you are very familiar with all the Zodiac evidence the correlations between the two is very compelling. You can also read my other post with comments about Nasar's biography of Nash and the Zodiac evidence. I wasn't even looking for the Zodiac killer when I read the biography. And there are so many theories and suspects Nash seems the most absurd but for someone who reads a lot and knows the Zodic case inside and out, it is very compelling.

Holger W said...

thanks for your comment. i'm very busy with work so i can't spend much time to the zodiac code for a couple of weeks, but i try to keep in.
i haven't read the Nash biography (sounds quit interesting) but i read about him an his work before i heard from the Zodiac. i don't believe that he's the guy who did the murder but there are some interesting facts. for example Nash has got an schizophrenic disorder. The Zodiac uses neologims like "christmass" in his letters. Neologism is a typical symptom of schizophrenia. Don't get me wrong, not every patient with schizophrenia uses neologism. Neologism indicates the formal thought disorder which is typical for schizophrenia. The Zodiac also talks about "slaves", "paradice" [neologism] and his "afterlife" this might be another sign for schizophrenia. these thoughts could be a delusion which is another typical symptom for schizophrenia. if you want to get more information about schizophrenia take a look to the "DSM" IV or V.

I'm positive about that Zodiac uses some kind of the "Playfair cipher" to encode his letters. In WWII the Germans an the British used it often. my grandfather was a radio operator in WWII he taught me a simple version of the Playfair cipher (in germany we call it "doppelkasten verschluesselung"). Even though the Germans had the "Enigma" the Playfair Cipher was their backup code and they used it quit often. But they made some mistakes. the radio messages mostly began and ended up with the same phrases, typical german correctness ;-) and they skipped the step of (we call it) "seriation". Seriation would have made it insolvable. All these things made it predictable and the allies could crack it nearly on real-time. So as you suggested the Zodiac would be predictable too.
Let me say one word to "Seriation". I don't know if it's the same word in english so i try to explain. You write down cleartext like Zodiac did (17 letters in a row without blanks) and than match the letters which stand about each other. Perhaps this is what he tried to show us in his halloween card with that single vertical "by". If he used "Seriation" we won't crack it ever.

John Cecil said...

Sylvia Nasar biography of Nash is amazing. It's a shame that no other Zodiac researcher bothered to read it. I'm not saying he did it, but there are too many direct references to both of them to dismiss. It is very compelling. Had Sylvia Nasar been familiar with the Zodiac case, as there is no reason she should have been, she would noticed the numerous connections. He was obsessed with the same numbers, was born on the 13th, mailed out identical letters and ciphers with identical content. It's not just a little, its a lot. He developed war strategies at RAND that were identical to what the Zodiac did, and even had cartoon characters of someone who would terrorize a city in the same way. I'm very familiar with the DSM IV. I'm just hoping more people would read it. If they don't think it's solid that's fine too.

Your background in ciphers is very interesting. I hope you can apply your knowledge to solving the cipher. Mine may be a partial solution at best, or more likely the right approach, searching for a mistake, as you said, and hopfully you can find a mistake, and maybe part of mine will be accurate.

Feel free to email me with any insights you have. cecil.john.mail (at)

randall clemons said...

boy i am glad you left your email..i sent you something i figured out a few days ago.i was looking for something on quadrant ciphers and found this. the quadrants are all things..dice...actual dice.para-dice..pair of dice..put a big zodiac cross right in the center of the look for the the first quadrant there are 0 the one right below it (1) quadrant thier is one on the top second quadrant (2) quadrant..their are 2 the 4th quadrant (3) quadrant thier are 3 dots.. 0,1,2,3... now draw squares around those dots including the 8 letters around this is tricky to explain with out a picture but in the 4th quadrant draw a square around the lowest dot in the one square around the the 2 dots about it ...there you have your dice..0,1,2,3.. it even says dice in the middle row going in the 4rth quadrant draw two more squares around each dot in the dye showing the number two and in all that bunch of 4 sqaures you will find the zodiac halloween card v symbol..i think you were on the right track indeed my friend..i think we have a very possible order for something...also i think you are right about the two keys is just what i would do plus the (secret pal) snow man card i think came with a pic of two not sure right off my head but i still have a gut feeling about it . i am going to do the most obvious transpositions and see what i get ten go fro there.. if this helps you to figure it out before i do just remember to give me a small shout out .. lol. i seriously hope this helps..either falls beyond the realm of coincedence. check you email and good luck.ive sent it to a few of the websites and the guys at were even impressed.

randall clemons said...

good idea publishing it on a blog.. i made one also. here is a link. it shows what i was trying to explain.

randall clemons said...

Mad Surf Media said...

I have just recently deciphered the 340 and I am talking with Napa PD. This is a false interpretation and my solution is self evident in accuracy. It does give the name and a bunch of other information. This and Starliper and any other attempt is entirely wrong. When it is confirmed I plan to publish, if you are a professional cryptographer, I would be willing to let you analyze it, but I need to know that my IP is protected.

Anonymous said...

To Mad Surf Media, and I have invented perpetual energy but will not let any engineers see it unless my IP is protected.

Anonymous said...

Yes Mad surf Media, like the Napa PD does anything but hide their own corruption.If anything, Napa Pd were involved in some of their own killing. Next

Anonymous said...

No one's used Greek alphabets? Many of the symbols are in ancient alphabets.

Jones said...

Hey, I'm just getting into this now and reading the popular zodiac book by day...reading online at night about the present tense case as it is....and I had the idea of a quadrant cipher but I know nothing about this stuff.

Anyhow the book just talked about how in one of the letters or something (to a cryptography professor or something, or maybe just one of the normal letters I have a poor memory for a few moments ago) that at the bottom of the letter or something it had 5 zodiac x's moving clockwise.....

Anonymous said...

Far too many variables! I don't get exactly what you show when I use Dave Oranchak's Webtoy. By the time I get to the fourth line it all starts turning to random gibberish.