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“Phi Spirals” – The Making of

Join me today as I make this ink and colored pencil mandala:


The beginning of this piece was the central square. I drafted 4 golden rectangles from each side of the square, and formed the corner squares. If the central square measures 1 by 1 unit, then the golden rectangles added to each side of the square equal 1 by .618... units. This makes the small corner square .618... x .618....

Let me teach you a little bit about PHI:

Φ = 1.618... and the lower case form Greek phi Didot.svg = .618..., or Φ minus 1. The "..." are present because the number never ends or repeats. Φ:1::1:Greek phi Didot.svg   Set 1 = a, Greek phi Didot.svg=b and then: a+b:a::a:b This last form is very common -  "a plus b is to a as a is to b". This defines the golden proportion, a very interesting number studied since antiquity.

An easier way to say this is that "The whole divided by the larger part is equal to the larger part divided by the smaller part."

By making each smaller square's side .618 times smaller I was able to construct the 4 spirals shown below. After that I created the octave pattern that you see going diagonally from top left to bottom right. I call it an octave because that is what it is called in music when the frequency doubles. Inside of one wave is two, and inside of that 2 more, and so on. Dividing by two creates the binary system of 2 4 8 16 32 64... etc.


Next I inked the spirals, and placed a flower of life pattern in one of them.


The next step was to ink the flower of life pattern and then use a pencil to divide the central octave pattern into the final 16 smaller waves.


After that I inked the 16 small waves and divided the other spiral into diminishing squares.

phispirals6 I created this tight "archimedian spiral" approximation by alternating between two center points. Once I was half a turn around the circle I switched the center hole and readjusted the compass. This almost spiral is precise enough for this jazz mandala.


By placing points every 137.51 degrees (the golden angle) around this fine spiral and connecting the dots, I was able to arrive at this sunflower like pattern for the third Spiral.phispirals9

I then finished the final spiral using different sizes of the flower of life pattern.phispirals10

The next step was to create the decomposed squares for the two corners.


After that it was time to color!  I blended colored pencils to get the gradients that you see. I also penciled in the bottom left corner's dual spiral pattern at this point. If you'd like to color all of my mandalas you can order my full 42 page coloring book here: Order Nowphispirals14

This part reminds me of an "Atom" at the end of this fibonacci spiral.


After some final touches the piece is finished.



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2 COMMENTS ON THIS POST To ““Phi Spirals” – The Making of”

  1. yaseen May 1, 2016 at 1:02 am

    You have obviously spent an enormous amount of time making these mandalas but did you find Yahovah Yahweh YaAllah or did you get lost in the maze?
    It comes as an absudity that Einstein should says, “the most incomprehensible thing about the universe is that it is comprehensible!”, because being of Jewish descent, he should have known better.
    YaAllah says, in the Qur’an, “They have forgotten the “Fact” of Creation.
    The reason why we, Adamkind, can understand the Universe is precisely because Yahweh taught Adam the names of everything in creation. It is a very special gift for mankind, and you have perefected it to understanfd how nature replicates things because you are a son of Adam, not a cat, a dog or other being.

    • sacredgeometryatx May 3, 2016 at 4:50 pm

      What I found was stronger critical thinking skills and deeper understanding of number =) As it says in euclid’s elements: “The whole is greater than the part”, and sacred geometry has helped to make me whole again.

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