The Alphabet Code: What Happens When You Run a Simple Rule on the Letter “a”
Here is a string of letters: gzhlvzggjzyihjgheqvzgzhlvzhlvbjzgyhzizygjzbjzhlvgjzehjdzzgheqv... It looks like a cat walked across a keyboard. It isn’t. It’s the start of a sequence that runs to thousands of characters, and every letter is fixed in advance by one rule applied to the letter “a.” No randomness, no guessing, no training data. Run the same rule again tomorrow, or on another computer,…
In the Engineering of Alphabets project, a sequence of letters is generated by applying a fixed rule to the letter "a" repeatedly. Each round replaces existing letters with new strings, causing the sequence to grow. The first seven rounds contain 1, 4, 14, 43, 138, 429, and 1,361 letters respectively. Mathematicians refer to this type of system as a substitution system.
The intriguing aspect of this project is that the rule is applied to the alphabet itself, which includes the 26 English letters along with their spoken names. By treating the alphabet as a mathematical system, interesting and unexpected structures can be observed.
The researcher generated several thousand letters using a computer program to analyze the output. The growth factor of the sequence, which represents the factor by which the sequence grows with each round, is found to be very close to the mathematical constant π (3.14159). This is not an exact match, but rather a close approximation, suggesting a potential connection between the alphabet and π.
Other notable findings include the sequence not settling into a loop, but instead exhibiting a steady growth in the number of distinct short phrases. This growth is roughly linear over the lengths checked, although it remains uncertain whether this pattern continues indefinitely. Additionally, 13 out of the 26 starting letters share a degree-13 polynomial, while the remaining 13 share a degree-14 polynomial.
The reason behind this split is still unknown and could potentially reveal deeper insights into the alphabet or the rule itself.
Written by urgent.news from Dev.to's reporting — not their text. Machine-written — may contain errors; check the original before relying on it.
