"DMT_15," digital + acrylic, April 17, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_14," digital + acrylic, April 16, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_13," digital + acrylic, April 15, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_12," digital + acrylic, April 14, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_11," digital+ acrylic, April 13, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
Just like with the Butterfly Fractal 1 (BF1), we are going to double everything, starting with Column 1 of the ODDs to give us Column 2 -- the first iterations of the EVENs.
What is special about the Col. 2 EVENs is that none of them are divisible by 4, and are called EVENs-NOT÷4.
Doubling Col. 2 gives Col. 3-- the second iteration of the EVENs, and this group ALL are divisible by 4 and are called EVENs÷4.
So far we have Columns 1-2-3 as ODDs--EVENs-NOT÷4--EVENs÷4. That's as complicated as it gets! (Well, not really. Let's just say it gets richer and richer!)
Notice that Row 1 is revealing our old friend the BF1 -- 1-2-4-...
More here___
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"DMT_10," digital + acrylic, April 12, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_9" digital + acrylic, April 11, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_8," digital + acrylic, April 10, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
Double your pleasure, double your fun
This matrix table has just begun!
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"DMT_7," digital re-working of acrylic, April 9, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
So far we have Columns 1-2-3... as ODDs--EVENs-NOT÷4--EVENs÷4. That's as complicated as it gets! (Well, not really. Let's just say it gets richer and richer!)
Notice that Row 1 is revealing our old friend the BF1 -- 1-2-4-...
Doubling Col. 2 gives Col. 3, doubling that Col. 4, doubling that Col. 5, and so on. ALL of these latter Columns are EVENs÷4.
More here___
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"DMT_6," digitally re-worked acrylic, April 8, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_5," digital re-working of acrylic, April 7, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
Something to ponder:
Sequentially divide any EVEN number by two -- it will result in an ODD. Divide any composite ODD -- it will result in a Prime. In the beginning, the source of all number patterns is the Primes.
How can we see this?
Let's make a matrix table:
Just like with the Butterfly Fractal 1 (BF1), we are going to double everything, starting with Column 1 of the ODDs to give us Column 2 -- the first iterations of the EVENs.
What is special about the Col. 2 EVENs is that none of them are divisible by 4, and are called EVENs-NOT÷4.
Doubling Col. 2 gives Col. 3-- the second iteration of the EVENs, and this group ALL are divisible by 4 and are called EVENs÷4.
So far we have Columns 1-2-3 as ODDs--EVENs-NOT÷4--EVENs÷4. That's as complicated as it gets! (Well, not really. Let's just say it gets richer and richer!)
Notice that Row 1 is revealing our old friend the BF1 -- 1-2-4-...
Doubling Col. 2 gives Col. 3, doubling that Col. 4, doubling that Col. 5, and so on. ALL of these latter Columns are EVENs÷4.
Thus, in our matrix table, each Column if simply double that of its predecessor.
ALL natural Whole Integer Numbers (WINs) are found in the Divisor (Factor) Matrix Table (DMT). It is called the DMT because it is a matrix of ALL ODDs, ALL EVENs_NOT÷4 and ALL EVENs÷4, and, ALL divisors (factors) of ANY WINs are found within!
As you can see, the top Row of the DMT is the BF1. The second Row is the BF1 times 3, the third Row is the BF1 time 5, the fourth Row is the BF1 time 7, and so on -- i.e. each Row is a sequential multiplication of the BF1 by its respective Col.1 ODD (1, 3, 5, 7, ...).
The BF1, you may recall, is nothing more than the sequence that is generated by the doubling of quantity 1 -- as represented by the Exponential Power of 2 (2ⁿ where n=0, 1, 2,... giving 1, 2, 4, ...) -- that when laid out with simple symbols like the number 1, or a grain of rice, or any other self-similar, re-iterative copy of itself, generates a "butterfly-like" fractal pattern. A pattern where any of the parts can be seen to form the whole and vice versa.
Within the DMT circle of ALL WINs is a much smaller subset of numbers that are ALL based on the BF1, i.e. they are all based on the Exponential Power of 2. We refer to the members of this set as "containers" because they are and act to hold a very select pattern of relationships that include another subset -- a subset of the subset of the DMT -- those exquisite and extremely rare Mersenne Prime - Perfect Number pairings, that to date equal 51!
A Mersenne Prime (Mp) is a Prime based on the Exponential Power of 2 (BF1).
A Perfect Number (PN) is number whose factors (divisors, not counting the number itself) that sum up to equal said number, e.i. PN 6 = 1+2+3.
A Mersenne Prime Square (MPS) is a square whose side = Mp = z, that subdivides into two rectangles, the PN and OC. The short side of the PN rectangle = x. Thus PN = xz and every Mp is paired with a PN!
When one tracks the Running Sums (∑) of the Column and Row values on the DMT, a whole Universe of connectivity explodes outward like the Big Bang itself! Talk about entanglement. Entanglements are the Conservation Laws -- most emphatically the Conservation of SpaceTime (ST) -- in action. The relationships between entanglement, entropy and time need clarification under the larger, even more encompassing umbrella, of ST -- and ST, along with the Conservation Laws, are based on symmetries -- you know -- of numbers!
More here___
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Comparison of three tables of natural whole numbers:
TOP: Divisor (Factor) Matrix Table (DMT) -- ALL numbers and their divisors, based on doubling the Columns and products of Axis.
MIDDLE: BBS-ISL Matrix (BIM) -- Inner Grid (IG) only contains EVENs÷4, based on the Inverse Square Law (ISL) and difference in Horizontal -Vertical Diagonal values, with Diagonals as the squares of the Axis values.
BOTTOM: Multiplication Table -- IG contains ALL numbers as products of Axis values with Diagonals as their squares.
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"DMT_4," acrylic, April 5, 2024, Reginald Brooks
correction: digital re-working over acrylic original
DMT = Divisor (Factor) Matrix Table
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"DMT_3" acrylic, April 4, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
Something to ponder:
Sequentially divide any EVEN number by two -- it will result in an ODD. Divide any composite ODD -- it will result in a Prime. In the beginning, the source of all number patterns is the Primes.
How can we see this?
Let's make a matrix table:
Just like with the Butterfly Fractal 1 (BF1), we are going to double everything, starting with Column 1 of the ODDs to give us Column 2 -- the first iterations of the EVENs.
What is special about the Col. 2 EVENs is that none of them are divisible by 4, and are called EVENs-NOT÷4.
Doubling Col. 2 gives Col. 3-- the second iteration of the EVENs, and this group ALL are divisible by 4 and are called EVENs÷4.
So far we have Columns 1-2-3 as ODDs--EVENs-NOT÷4--EVENs÷4. That's as complicated as it gets! (Well, not really. Let's just say it gets richer and richer!)
Notice that Row 1 is revealing our old friend the BF1 -- 1-2-4-...
Doubling Col. 2 gives Col. 3, doubling that Col. 4, doubling that Col. 5, and so on. ALL of these latter Columns are EVENs÷4.
Thus, in our matrix table, each Column if simply double that of its predecessor.
ALL natural Whole Integer Numbers (WINs) are found in the Divisor (Factor) Matrix Table (DMT). It is called the DMT because it is a matrix of ALL ODDs, ALL EVENs_NOT÷4 and ALL EVENs÷4, and, ALL divisors (factors) of ANY WINs are found within!
As you can see, the top Row of the DMT is the BF1. The second Row is the BF1 times 3, the third Row is the BF1 time 5, the fourth Row is the BF1 time 7, and so on -- i.e. each Row is a sequential multiplication of the BF1 by its respective Col.1 ODD (1, 3, 5, 7, ...).
The BF1, you may recall, is nothing more than the sequence that is generated by the doubling of quantity 1 -- as represented by the Exponential Power of 2 (2ⁿ where n=0, 1, 2,... giving 1, 2, 4, ...) -- that when laid out with simple symbols like the number 1, or a grain of rice, or any other self-similar, re-iterative copy of itself, generates a "butterfly-like" fractal pattern. A pattern where any of the parts can be seen to form the whole and vice versa.
Within the DMT circle of ALL WINs is a much smaller subset of numbers that are ALL based on the BF1, i.e. they are all based on the Exponential Power of 2. We refer to the members of this set as "containers" because they are and act to hold a very select pattern of relationships that include another subset -- a subset of the subset of the DMT -- those exquisite and extremely rare Mersenne Prime - Perfect Number pairings, that to date equal 51!
A Mersenne Prime (Mp) is a Prime based on the Exponential Power of 2 (BF1).
A Perfect Number (PN) is number whose factors (divisors, not counting the number itself) that sum up to equal said number, e.i. PN 6 = 1+2+3.
A Mersenne Prime Square (MPS) is a square whose side = Mp = z, that subdivides into two rectangles, the PN and OC. The short side of the PN rectangle = x. Thus PN = xz and every Mp is paired with a PN!
When one tracks the Running Sums (∑) of the Column and Row values on the DMT, a whole Universe of connectivity explodes outward like the Big Bang itself! Talk about entanglement. Entanglements are the Conservation Laws -- most emphatically the Conservation of SpaceTime (ST) -- in action. The relationships between entanglement, entropy and time need clarification under the larger, even more encompassing umbrella, of ST -- and ST, along with the Conservation Laws, are based on symmetries -- you know -- of numbers!
More here___
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"DMT_2," acrylic, April 3, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
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"DMT_1," acrylic, April 2, 2024, Reginald Brooks
DMT = Divisor (Factor) Matrix Table
Something to ponder:
Sequentially divide any EVEN number by two -- it will result in an ODD. Divide any composite ODD -- it will result in a Prime. In the beginning, the source of all number patterns is the Primes.
How can we see this?
Let's make a matrix table:
Just like with the Butterfly Fractal 1 (BF1), we are going to double everything, starting with Column 1 of the ODDs to give us Column 2 -- the first iterations of the EVENs.
What is special about the Col. 2 EVENs is that none of them are divisible by 4, and are called EVENs-NOT÷4.
Doubling Col. 2 gives Col. 3-- the second iteration of the EVENs, and this group ALL are divisible by 4 and are called EVENs÷4.
So far we have Columns 1-2-3 as ODDs--EVENs-NOT÷4--EVENs÷4. That's as complicated as it gets! (Well, not really. Let's just say it gets richer and richer!)
Notice that Row 1 is revealing our old friend the BF1 -- 1-2-4-...
Doubling Col. 2 gives Col. 3, doubling that Col. 4, doubling that Col. 5, and so on. ALL of these latter Columns are EVENs÷4.
Thus, in our matrix table, each Column if simply double that of its predecessor.
ALL natural Whole Integer Numbers (WINs) are found in the Divisor (Factor) Matrix Table (DMT). It is called the DMT because it is a matrix of ALL ODDs, ALL EVENs_NOT÷4 and ALL EVENs÷4, and, ALL divisors (factors) of ANY WINs are found within!
As you can see, the top Row of the DMT is the BF1. The second Row is the BF1 times 3, the third Row is the BF1 time 5, the fourth Row is the BF1 time 7, and so on -- i.e. each Row is a sequential multiplication of the BF1 by its respective Col.1 ODD (1, 3, 5, 7, ...).
The BF1, you may recall, is nothing more than the sequence that is generated by the doubling of quantity 1 -- as represented by the Exponential Power of 2 (2ⁿ where n=0, 1, 2,... giving 1, 2, 4, ...) -- that when laid out with simple symbols like the number 1, or a grain of rice, or any other self-similar, re-iterative copy of itself, generates a "butterfly-like" fractal pattern. A pattern where any of the parts can be seen to form the whole and vice versa.
Within the DMT circle of ALL WINs is a much smaller subset of numbers that are ALL based on the BF1, i.e. they are all based on the Exponential Power of 2. We refer to the members of this set as "containers" because they are and act to hold a very select pattern of relationships that include another subset -- a subset of the subset of the DMT -- those exquisite and extremely rare Mersenne Prime - Perfect Number pairings, that to date equal 51!
A Mersenne Prime (Mp) is a Prime based on the Exponential Power of 2 (BF1).
A Perfect Number (PN) is number whose factors (divisors, not counting the number itself) that sum up to equal said number, e.i. PN 6 = 1+2+3.
A Mersenne Prime Square (MPS) is a square whose side = Mp = z, that subdivides into two rectangles, the PN and OC. The short side of the PN rectangle = x. Thus PN = xz and every Mp is paired with a PN!
When one tracks the Running Sums (∑) of the Column and Row values on the DMT, a whole Universe of connectivity explodes outward like the Big Bang itself! Talk about entanglement. Entanglements are the Conservation Laws -- most emphatically the Conservation of SpaceTime (ST) -- in action. The relationships between entanglement, entropy and time need clarification under the larger, even more encompassing umbrella, of ST -- and ST, along with the Conservation Laws, are based on symmetries -- you know -- of numbers!
More here___
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DMT_1," acrylic, April 1, 2024, Reginald Brooks
correction: digital, not acrylic
DMT = Divisor (Factor) Matrix Table
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