How can I determine the percentage of entries which are even in a Sierpinski Triangle?
$begingroup$
I know that the even numbers of pascal's triangle form the Sierpinski Triangle. I also know that as we add more columns (or rows) depending on how you look at it, the even numbers cluster together. I have this picture:
Am I correct in assuming this is basically Pascal's triangle and that the even numbers are the black squares and that the odd numbers are the even squares?
My actual question is: How can I come up with a formula that gives the percentage of entries which are even based off the number of columns which are in the triangle.
I have this table where the left column gives the number of columns in the triangle while the right columns gives the percentage of entries which are even.
7 25.
15 40.4412
31 53.9773
63 64.9519
127 73.5102
255 80.0553
511 85.0123
1023 88.7483
My approach would be to use the finite differences method to generate a polynomial but I don't think that would be appropriate since it would only give me one of many polynomials that it could be.
My final goal would be to implement this in Mathematica
sierpinski-numbers
asked Jan 14 at 0:51
user130306user130306
45319
$endgroup$
add a comment |
$begingroup$
I know that the even numbers of pascal's triangle form the Sierpinski Triangle. I also know that as we add more columns (or rows) depending on how you look at it, the even numbers cluster together. I have this picture:
Am I correct in assuming this is basically Pascal's triangle and that the even numbers are the black squares and that the odd numbers are the even squares?
My actual question is: How can I come up with a formula that gives the percentage of entries which are even based off the number of columns which are in the triangle.
I have this table where the left column gives the number of columns in the triangle while the right columns gives the percentage of entries which are even.
7 25.
15 40.4412
31 53.9773
63 64.9519
127 73.5102
255 80.0553
511 85.0123
1023 88.7483
My approach would be to use the finite differences method to generate a polynomial but I don't think that would be appropriate since it would only give me one of many polynomials that it could be.
My final goal would be to implement this in Mathematica
sierpinski-numbers
asked Jan 14 at 0:51
user130306user130306
45319
$endgroup$
$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11
add a comment |
$begingroup$
I know that the even numbers of pascal's triangle form the Sierpinski Triangle. I also know that as we add more columns (or rows) depending on how you look at it, the even numbers cluster together. I have this picture:
Am I correct in assuming this is basically Pascal's triangle and that the even numbers are the black squares and that the odd numbers are the even squares?
My actual question is: How can I come up with a formula that gives the percentage of entries which are even based off the number of columns which are in the triangle.
I have this table where the left column gives the number of columns in the triangle while the right columns gives the percentage of entries which are even.
7 25.
15 40.4412
31 53.9773
63 64.9519
127 73.5102
255 80.0553
511 85.0123
1023 88.7483
My approach would be to use the finite differences method to generate a polynomial but I don't think that would be appropriate since it would only give me one of many polynomials that it could be.
My final goal would be to implement this in Mathematica
sierpinski-numbers
asked Jan 14 at 0:51
user130306user130306
45319
$endgroup$
I know that the even numbers of pascal's triangle form the Sierpinski Triangle. I also know that as we add more columns (or rows) depending on how you look at it, the even numbers cluster together. I have this picture:
Am I correct in assuming this is basically Pascal's triangle and that the even numbers are the black squares and that the odd numbers are the even squares?
My actual question is: How can I come up with a formula that gives the percentage of entries which are even based off the number of columns which are in the triangle.
I have this table where the left column gives the number of columns in the triangle while the right columns gives the percentage of entries which are even.
7 25.
15 40.4412
31 53.9773
63 64.9519
127 73.5102
255 80.0553
511 85.0123
1023 88.7483
My approach would be to use the finite differences method to generate a polynomial but I don't think that would be appropriate since it would only give me one of many polynomials that it could be.
My final goal would be to implement this in Mathematica
sierpinski-numbers
sierpinski-numbers
asked Jan 14 at 0:51
user130306user130306
45319
asked Jan 14 at 0:51
user130306user130306
45319
asked Jan 14 at 0:51
user130306user130306
45319
asked Jan 14 at 0:51
user130306user130306
45319
asked Jan 14 at 0:51
user130306user130306
45319
45319
$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11
add a comment |
$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11
$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11
$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11
add a comment |
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$begingroup$
Maybe Ask if it exist on the mathematica stackexchange.
$endgroup$
– Roddy MacPhee
Feb 26 at 17:11