# How to draw Samtaegeuk (yin-yang symbol but with three swirls, each a different colour)?

I'm trying to draw a Samtaegeuk symbol, which is essentially a yin-yang symbol with three swirls, each one a different colour.

I found the guide below for drawing the two-swirl Korean taegeuk, but I need something similar for the three-swirl one.

• Hi. Welcome to GDSE. Are you asking about drawing this by hand, or using graphic design software such as a vector image editor, and if so, which software do you have? May 3, 2023 at 17:26

No Software . . .

If you want to draw it by hand, and make it easy for yourself, then get some equilateral triangle (aka isometric) grid paper, or print some out if you have a printer.

Use a compass to draw a circle and a ruler for the lines. Create guides exactly as shown below left, and then draw arcs by hand between these points to make approximate spirals as shown below right. If drawing spiral arcs like this is difficult for you, one possibility is to use a set of French Curves as a drawing aid.

Click to view larger

• +1 Ya know.. I knew there had to be a way to utilize triangles here.. I just couldn't come up with it. Nice job `:)` May 4, 2023 at 0:31
• looks fine! are those arcs circular arcs? Is this a result of your own reasoning or have you seen a how-to-draw-it ? May 4, 2023 at 11:51
• Where are the centres of those arcs located? Hard to draw with a compass if you don't know where one side of it goes. May 4, 2023 at 13:23
• @Wasserbest - no not circular, this only a method for approximating spirals by drawing by hand. If accuracy is required, then it would be better to use vector software. This is my own idea. May 4, 2023 at 15:34
• @nick012000 - my answer doesn't say to draw the arcs with a compass. It says to draw "a circle". This is a method for drawing approximate spirals by hand. I have added extra details to make this clear now. If accuracy is required it would be better to use vector software to draw it. I included this answer because the OP did not say if they were using software or not. May 4, 2023 at 15:43

You can get something resembling easily by drawing 3 equal, but 120 degrees rotated spirals which start from the center, a circle around them and by filling the areas with the shape builder.

It's tricky to copy from a screenshot manually the right spiral shapes with the pen. I'm not claiming it's impossible, but well trained hands and eyes are a must. I'll show an example later.

Someone may know a twisting filter which creates the right curves from straight lines or twists a colored 3-sector pie diagram. Another may know how to create them in math or how the drawing process is geometrically specified in some fraternity rulebook. I use Illustrator's logarithmic spiral tool, guessing, trial and error:

In the left there's a 4 segment spiral. The initial radius is 50 mm and the decay factor is 62%.

In the right 120 and 240 degrees rotated spiral copies are made. The copies are moved to end to the same point. The endpoints snap if you drag them (after selecting the spiral) with the white arrow. As well you can set the rotation center to the endpoint of the 1st spiral and rotate twice with option copy = ON.

The outline of your shape is a circle. The spiral decay factor 62% was found after a couple of attempts. That 62% made possible to draw the green circle which meets quite nicely the spirals:

As you see, It's not exact, but maybe it fits visually well enough. In the right the excessive tails of the spirals are removed and the areas inside the circle are filled with your colors. Killing the spiral extras outside the circle and forming closed shapes inside the circle are both done by using the shape builder. A tiresome alternative is to split and join paths.

Logarithmic spiral is not a perfect idea. It's too curved in the center and straightens too fast further. Ill try another old trick to get a better curves which are straighter at the center, but fit well the outline circle at the edge.

At first I make the promised attempt to draw the spirals manually on your image:

One white spiral is drawn with the pen and 2 rotated copies are made:

The drawn spiral has only 3 anchors. One at both ends and one in the middle. It was quite easy to make the curve look regular. As you see, it's off several pixels. That could be improved by inserting more anchors, but making it look regular starts to need some real skill.

This is near the center less off than the log spiral version, so try this as your 1st attempt.

My last attempt uses custom art brush to get a curve which is nearly straight near the center, but further it approaches the outline circle.

In the left there's a 100 mm diameter circle. Its cut with the scissors at 12 and 3 o'clock anchor points. The smaller piece is moved a little aside.

The smaller piece is dragged to brushes and defined to be and art brush. The brush direction is set to L-R. The auto-stretch to the path length is ON. The bigger piece is scaled to exact 50% size. The new brush is applied to it. The result is in the middle.

In the right the appearance is expanded to fix the brush effect and 120 and 240 degrees rotated copies are made and placed to snap at the endpoint like the log spirals in the 1st attempt.

In the next image a 100 mm diameter green circle is drawn to the center point. It should in theory meet the curve ends exactly:

In the right fillable areas are formed with the shape builder and filled with your colors. In theory no remnants should be left. Illustrator's circles are not exactly round and the shape builder also has some tolerance. For these reasons I found three about 10 mm long arcs as remnants from the shape building. I deleted them and that's it.

For me this looks even better than what's got by drawing the spiral manually on your image. In theory the manually drawn spiral should look perfect, but I made it too simple to avoid the common irregularity problems of manually drawn multiple anchor Bezier curves.

It's somewhat easy and only requires you to draw a couple circles.

1. Draw circle with crosshairs to mark the center (you can merely use guides if desired)
2. Draw a smaller circle inside the larger one so it touches the top edge and the center point of the large circle.
3. Delete the left anchor point of the smaller circle, creating a half-circle arc
4. Select the arc and choose `Effect > Distort & Transform > Transform` from the menu
5. In the effect dialog window, enter `360/3` in the `Angle` field (you want to divide the circle by 3 parts) -- Enter `2` in the `Copies` field (You want 2 more arcs) -- and set the 9-point origin to the bottom left corner, so that rotation begins from the big circle's center. Ticking `Preview` should show you the rotations correctly. Then hit `OK`.
6. Select the original arc and choose `Object > Expand Appearance` to "bake in" the effect.
7. Delete the crosshair paths
8. Use the Live Paint Bucket or Shape Builder tools to fill in color

I do realize this doesn't have the small, tight, arcs as in your example... I'm still playing with it to see if there's some straightforward method for smaller arcs other than merely manually drawing the first arc, then rotating 120° and 240°... which is fairly easy in itself if familiar with bezier tools.

Okay.. smaller parts.... Just need to draw a 3 circles and align them all on center....

(Right-click the image and choose "open in new window/tab" to see it larger)

The middle circle in the above doesn't have to hit the 50% point of the large circle radius, you can make it larger (or smaller) if desired. The important piece is that small circle needs to align with the top edge of the middle circle and the center point of the largest circle.

Example:

It's also possible to not use perfect circles, but more oblong or elliptical shapes for the inner areas....

The steps are all the same.

• .. probably went overboard here.. but I was having fun playing with it.. May 3, 2023 at 23:44

The samtaegeuk is a symbol holding deep and complex cultural meaning in Korea, which goes well beyond my knowledge. The following Python code generates a similar shape with 2, 3, or an arbitrary number of lobes. Perhaps tweaking the parameters (particularly the colors and the function `th(r)`) will be a helpful starting point for those interested in approaching this via computer graphics.

``````from math import pi, sin, cos, exp, sqrt
import drawsvg as draw

def flatten(l):
return [item for sublist in l for item in sublist]

width = 512
lobes = 3
steps = 150

def th(r):
return 2*pi*0.1*r*exp(r)

w = 0.49*width
dth = 2*pi/lobes
rads = [k/steps for k in range(steps)]

d = draw.Drawing(width, width, origin='center')

for k in range(lobes):
leading =  [(w*r*cos(th(r) + k*dth), w*r*sin(th(r) + k*dth)) for r in rads]
outer =    [(w*cos(th(1) + (k + x)*dth), w*sin(th(1) + (k + x)*dth)) for x in rads]
trailing = [(w*r*cos(th(r) + (k + 1)*dth), w*r*sin(th(r) + (k + 1)*dth)) for r in reversed