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"DMT_27," digital + acrylic, April 29, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

Ah, the color purple -- or is it violet

The green before informs it all,

Or does it? Just look at that orange.

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"DMT_26," digital + acrylic, April 28, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

How hard is it to make the table? Easy -- on a napkin, back of an envelope or any spreadsheet app -- simply make the 1st Column the ODDs, double that to make the 2nd, double that to make the 3rd...

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"DMT_25," digital + acrylic, April 27, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

No worries if you get lost. Every number is here. Pick any number, divide it by 2 until you end with an ODD. The divisors of said number are those values + the same number of values in Row 1 + the same number of values in any of the *composite ODDs. *If said number divides down to a composite number, then include this Row + other Rows whose ODD(s) are the Prime factors of that initial ODD.

Example: say 13684

13684÷2=6842

6842÷2=3421 and there are two divisions required to reveal the ODD and thus three DMT cell values

3421 is a composite number: 1-11-311-3421 so you include the ODD Rows 1-11-311-3421 three DMT cell values across.

1-2-4

11-22-44

311-622-1244

3421-6842-13684

The DMT is a simple and always ready visualization. Dance!

Example2: 13864

Divides down to 1733, 3466, 6932, 13864 or 4 DMT cell values with the ODD 1733 being Prime.

1-2-4-8

1733-3466-6932-13864

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"DMT_24," digital + acrylic, April 26, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_23," digital + acrylic, April 25, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

Fractal entanglement is inescapable.

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"DMT_22," digital + acrylic, April 24, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

Row 1 = Butterfly Fractal 1 = BF1 = simple doubling of quantity, starting with 1.

Pick a number, say 8. What are its divisors? 1-2-4-8.

Pick another number, say 10. Divisors? 5-10 and 1-2. Why? You must match BF1 values with #.

Pick number 20. Divisors? 5-10-20 and 1-2-4. Notice the cross symmetry!

Pick # 40. Divisors? 5-10-20-40 and 1-2-4-8.

Pick # 80. Divisors? 5-10-20-40-80 and 1-2-4-8-16.

Pick #72. Divisors? 9-18-36-72 and 3-6-12-24 and 1-2-4-6. Why the extra middle Row? If the # Row divides down to a composite ODD, you include the divisor's Row(s) factors in the tally.

ODD number divisors are different: Primes have only 1 and themselves, composites are made of Primes, so we grab them individually out of the ODDs Column.

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"DMT_21," digital + acrylic, April 23, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_20," digital +vacrylic, April 22, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

If you accept the 1st fractal Row -- 1-2-4-8-16... -- then nothing is gained by doubling it. There are no new numbers.

If you triple it -- multiply the whole Row by 3 -- forming the 2nd fractal Row, you get 3-6-12-24-48.... Again, multiplying the 1st Row by 4 yields no new numbers.

If you multiply it by 5 -- multiply the whole Row by 5 -- forming the 3rd fractal Row, you get 5-10-20-40-80.... And so on.

Multiplying the 1st fractal Row by each of the ODD number sequence values in the 1st Column fills out the entire DMT and within it are found ALL the natural whole numbers and ALL their divisors.

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"DMT_19," digital + acrylic, April 21, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_18," digital + acrylic, April 20, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_17,"digital + acrylic, April 19, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_16," digital + acrylic, April 18, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"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-...

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