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Created using "Purple Sunflower Burst":

Color shifting Metatron's Cube with fibonacci spirals:

Double Spirals Animated:

Double spirals 2:

Double Spirals 3:

Double Spirals 4:

Egg of Life:

Flower of Life Divided:

Seed of Life:

Flower of life on Fire:

Flower of life:

Metatron's Cube:

Octahedron - one of the 5 platonic solids:

Op art style geometry:

Phi Spirals:

Op art style Lenticular Print:

Threnody for Evan Boy - RIP

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]]>Today I will share with you how I created this 20" x 30" mixed media painting:

Here is the original sketch. The main details are the five golden spirals and the pentagonal symmetry of the center.

Notice in the sketch how there is a large pentagon containing the golden spirals. Each of these spirals is within a golden parallelogram. This is kind of like a golden rectangle, except the angles are not 90 degrees. This all happens because Phi (Fibonacci) is present in all pentagonal forms. This leads to the unique fractal quality of pentagons and pentagrams. A pentagon can be infinitely divided into itself with pentagrams that reduce by the golden ratio. It can also grow infinitely:

I really wanted to layer the five pattern over top of the flower of life's sixfold pattern. I sketched the flower of life and pentagon pattern with pencil then inked my ideas. To make the background I cut out a piece of paper in a circle to so that I could mask the center. I used a splattering technique of red, yellow, and violet watercolors. After they dried I colored the curved triangles with red and violet colored pencils. The lighter white petals with splatters that make up the flower of life is really the paper showing through. Using colored pencils over ink and watercolor was a fun layering technique to use. The next step was to add the bottom layer of watercolor to the center of the mandala. The overlap of the five and six in the center can throw the eye off!

Next I used colored pencils to color the very center of the mandala. I had to shade it just right to get the five sided star that overlaps the six petaled flower to look correct. I really wanted the forms to appear slightly translucent.

A side note: I really like to make animations with my artwork! This is one of the animated gifs that I made with this piece:

If you enjoyed that and have the time here is a video with music that features 11 of my pieces animated. If not, please continue reading how I made this piece.

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At this point I didn't know what to do and started to color the flower of life that fills the ends of the spirals. That's when I realized that I wanted to add one more pattern! This new pattern started by dividing the circle in 32 parts. I achieved this by dividing it in 2, then 4, 8, 16, and then 32 parts. Next I drew squares offset by 45 degrees towards the center. Then I divided the circle into quasi squares (concentric circles divided by 32 radial lines) and connected the corners with these spirals that you see.

The next step was to draw the same kind of spirals going the opposite way.

After that I placed one circle into each new quasi square.

This is what is looks like after inking the circles in:

Next I painted all of the circles with colored pencils, blending from red to yellow.

Here is more of it colored with colored pencils:

I colored the dark background behind the spirals and after some other final touches it was complete!

Click here to order the shirt that features this painting.

That's not the end of it though! I made the piece "Alchemical Marriage" as a sister piece to this one. I will be writing a post soon on how I made Alchemical Marriage!

Here is another animation of mine:

I ended up enjoying this piece so much that I also made this blanket from it! If you like my art and would like to go on a magic carpet ride my blanket is now available! It's woven, not printed, and made in the USA from super thick cotton.

**What the painting means:**

The marriage of five to six. The centerpiece is a five sided star that contains five golden parallelograms that overlaps the seed of life. The seed of life makes up the flower of life and if you connect all the points of the flower of life you get triangles that make up hexagons. This five against six I feel is representative of the merging of heaven and earth. The pattern of division that creates the yellow dots filling the 5 golden spirals are based on a binary pattern of division. Dividing by 2 so to speak. 2 - 4 - 8 - 16 - 32 - There are 32 circles around in each radial row. This is a system of octaves. In music there are 7 tones in a scale and the 8th is the same again - the octave higher is double the frequency, or 1/2 of the frequency is 1 octave lower. So 2 - 4 - 8 - 16 - 32 supports the octave structure of music. The ratio is 1:2 for this. Other intervals (distances between notes) exist other than octaves and these are defined as other simple ratios such as 2:3, 3:4, 4:5, 5:6, 8:9, and more. The ratio 4:5:6 defines a major chord, therefore this painting can be interpreted as the ratios for a musical major chord because 4, 5, and 6 are present and overlapping. As a musician and artist I like to think of my artwork as frozen music, containing musical polyrhythms and intervals (overlapping ratios). After all the word rational comes from the word ratio! Our modern music system does not use these pure ratios as key changes don't sound good. We use what is called equal temperament which makes all the keys evenly out of tune. The wellhead of american music is a blues man, steel guitarists, slide guitarists, singers, or other instrumentalists who hit one of those sweet variably tuned notes.

I hope you enjoyed how this painting relates to music. =) All of this relates to the seven liberal arts that may liberate your mind known as the trivium and quadrivium. The trivium is grammar (input), logic (processing) and rhetoric (output). This is how to learn. We see, hear, read, and perceive. After that we apply logic. Finally the rhetoric stage is telling others what we have learned. To teach is to understand is to learn is to know. The quadrivium is number theory (pure number) geometry (number in space) music (number in time) and astronomy (number in space and time - traditionally referred to as cosmology). These are the lost tools of learning - and how to apply them to number.

-Ansel Bickerton

Sacred Geometry Artist

]]>Today you will see how I made this piece titled “Synthesis of the Tetractys and Tree of Life”.

A friend and I were speaking about the Tetractys and how it was a sort of tree of life for the Pythagoreans (ancient greeks who were followers of pythagoras) - especially being that the ten aspects of the Tetractys can been seen to correlate with the ten Sephirot (attributes) of the Kaballistic Tree of Life. Knowing that both the Tetractys and the Tree of Life fit into the flower of life separately, I realized that it must be possible for them to fit together. Soon I had this small sketch showing how I envisioned them. The larger triangle made of ten points that starts with one point at the top is the Tetractys. Each lower row has two, then three, and finally four dots. 1+2+3+4=10 This forms a perfect triangle of ten. In the center is the tree of life, which shares three dots with the Tetractys. Each Sephirot (attribute) is a representation of the infinite through which the physical and metaphysical realms are constantly emanating.

To start the piece I found the center of my paper and then drew two perpendicular lines. After this I drew a large flower of life pattern and a larger circle that holds three of the smaller circles within it's diameter.

Next I drew a smaller flower of life pattern that is one half of the size of the first. Each “petal” holds two smaller petals.

The next step was to layout a grid of equilateral triangles for my representation of the Tetractys. This was easy to achieve, as the flower of life grid creates equilateral triangles if you connect the centers of each flower. This is one of the uses of the flower of life - creating a theoretically perfect grid of equilateral triangles.

I then added an even smaller flower of life layer within this triangle. The circles are again one half the size of the last flower of life pattern that I drew.

Next I inked the outer circle.

Here is the larger flower of life inked in:

I then added all seventeen circles - seventeen because the Tetractys and Tree of Life each have ten, but share three in my depiction.

Next I added the lines that connect all the sephirot in the tree of life - 22 connections - 1 for each letter of the ancient Hebrew alphabet.

I then finished inking the piece and used watercolors to paint the background colors. Once the watercolor dried I used colored pencils to add another layer of color. All that was left was some final touches and that's it! I hope you enjoy seeing how I make my artwork.

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]]>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 = .618..., or Φ minus 1. The "..." are present because the number never ends or repeats. Φ:1::1: Set 1 = a, =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.

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.

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

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 Now

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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Today I will show you how I painted this sunflower inspired piece titled "Purple Sunflower Burst".

The beginning - first let me tell you about the surface this painting was done on. This was my first time working with claybord (that's how it's spelled). It's a surface meant for many mediums, and I chose it because it was extremely smooth - it's not easy to do fine details on a rough surface.

The first step: I used a pencil to draw straight lines from corner to corner of my square. This gave me diagonals and a center. I then used a compass to bisect each 90 degree angle into a 45 to create the verticals and horizontals that pass through the center. After that I needed to divide my pie into 90 equal divisions! This is what you see below. By dividing it into 45 parts first and then dividing each of those by two I made it simpler to cut this pie into 90 pieces. With trigonometry you can find the length from one division to the next on the circumference. Look at it as 45 triangles, each with an end near the center measuring 8 degrees. Cut one of these triangles in half and we have two right triangles - each with an angle of 4 degrees, and an angle of 90 degrees. Measure your radius and we now have two angles and a side! This means the sine of 4 degrees times the radius equals 1/2 of the distance we are looking for! (sine is a trigonometry function of right triangles)

I walked this distance around the circle starting at the top going both ways all the way around. If you are off slightly in setting your compass you will find the correct locations will be directly in the middle of the two marks you made from going around both ways. Conveniently these circles intersect each others centers providing the middle points to add the other 45 divisions to make the full 90 .

Why 90 divisions? Because I am making spirals based off of the fibonacci sequence. It is 1 1 2 3 5 8 13 21... I am using 3:5 as my basic ratio to approximate phi. Multiplying 3 and 5 by 6 gives me 18 and 30, so I will have 18 spirals one way, and 30 the other. 90 happens to be the lowest common multiple of 18 and 30 (18 goes into 90 five times, and 30 goes into 90 three times.

The next step: creating concentric circles to make a quasi square grid. These are the lighter concentric circles you see. To make these I make the width of each square equivalent to the width, each set of quasi squares getting smaller towards the center. This is my grid to place points. On the outer rim I started at the very top with a singular point. I went every three around the circumference to get 30 dots, and every 5 around to get 18 dots. Then for the 30 dots I counted towards the center 5 squares and over 3 squares. I did this over and over again until all the points were plotted for all 30 spirals. Then I plotted the points for the other 18 spirals - only inverting the slope this time - 3 squares toward the center and five squares over. Less spirals means shallower angle. Again with 3:5! Finally I was able to connect all the dots and place each circle in its appropriate place.

Here is another picture:

Next I used ink to darken all of the circles. After that I used brushes and sponges to create an abstract background layer with acrylic paint. Then I started work on coloring the spheres. I used many translucent layers of paint called glazes to get them just right. It takes a while, but I really love the depth it gave to the spheres. It allows the background to show through at points making the spheres look translucent.

Some of the spheres up close: Have a wonderful day and thank you for taking the time to view my artwork. - Ansel Bickerton

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