HomeWorldData[OC] (Collatz Conjectur) – Difference of the number of 1s in binary form before and after the corresponding operation averaged for numbers 1 to 1 billion, averages taken every 1000 numbers.
[OC] (Collatz Conjectur) – Difference of the number of 1s in binary form before and after the corresponding operation averaged for numbers 1 to 1 billion, averages taken every 1000 numbers.
August 23, 2024
[OC] (Collatz Conjectur) – Difference of the number of 1s in binary form before and after the corresponding operation averaged for numbers 1 to 1 billion, averages taken every 1000 numbers.
Posted by hergendy
6 comments
I generated the data based on my assumption that if it is expected to converge to the 1-4-2-1 looping sequence, the numbers represented in binary will always converge to 001-100-010-001 numbers that have only one ‘1’ digit present in them, they would always have to show decreasing ‘1’ present after operations on average.
On the 3x+1 operation you are basically shifting by one to the left and adding it to the original number and adding a 1 in the end as well. On the division by 0 you are basically shifting the whole number by 1 to the right. This operation never reduces the amount ‘1’s present.
The frequency of the spikes follows a logarithmic pattern, doubling in distance every time. (~2.22*10^7, ~4.45*10^7, ~8.95*10^7, ~1.79*10^8, ~3.577*10^8, ~7.158*10^8)
This is all just a vague guess from my part and decided to quickly plot it, to see what it looks like.
* C# for loop used to generate data into csv * Python pandas and matplotlib used to read the csv plot the data
I have no idea what this is!
I’m intimately familiar with both the conjecture and binary numbers. I have no idea what I’m looking at here.
Schizophrenia claims another soul.
If you think there is a mysterious “pattern” repeating itself you should go back to it and try to understand more clearly what you are doing ^^
Nice effort but if you google the Collatz conjecture you’ll find hundreds and hundreds of plots and graphs, some of them identical to yours.
6 comments
I generated the data based on my assumption that if it is expected to converge to the 1-4-2-1 looping sequence, the numbers represented in binary will always converge to 001-100-010-001 numbers that have only one ‘1’ digit present in them, they would always have to show decreasing ‘1’ present after operations on average.
On the 3x+1 operation you are basically shifting by one to the left and adding it to the original number and adding a 1 in the end as well.
On the division by 0 you are basically shifting the whole number by 1 to the right. This operation never reduces the amount ‘1’s present.
The frequency of the spikes follows a logarithmic pattern, doubling in distance every time. (~2.22*10^7, ~4.45*10^7, ~8.95*10^7, ~1.79*10^8, ~3.577*10^8, ~7.158*10^8)
This is all just a vague guess from my part and decided to quickly plot it, to see what it looks like.
* C# for loop used to generate data into csv
* Python pandas and matplotlib used to read the csv plot the data
I have no idea what this is!
I’m intimately familiar with both the conjecture and binary numbers. I have no idea what I’m looking at here.
Schizophrenia claims another soul.
If you think there is a mysterious “pattern” repeating itself you should go back to it and try to understand more clearly what you are doing ^^
Nice effort but if you google the Collatz conjecture you’ll find hundreds and hundreds of plots and graphs, some of them identical to yours.