Journals #02 - Basics of Geometric Design | 4 & 8 fold symmetry | Dearing Wang | Skillshare

Journals #02 - Basics of Geometric Design | 4 & 8 fold symmetry

Dearing Wang, I grew up with a pen in my hand.

Journals #02 - Basics of Geometric Design | 4 & 8 fold symmetry

Dearing Wang, I grew up with a pen in my hand.

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10 Lessons (40m)
    • 1. Introduction of Four & Eightfold symmetries

    • 2. How to Build a Four fold Diagram | Diagram #01

    • 3. How to Build an Eight Fold Diagram | Diagram #02

    • 4. Adding 4 fold & 8 fold diagrams to our Sketchbook

    • 5. Four Snubbed Leafs | Diagram #9

    • 6. Eight Snubbed Leafs | Diagram #10

    • 7. Alternative Method of Eightfold diagram

    • 8. Four circles | Diagram #11

    • 9. Eight circles | Diagram #12

    • 10. Recap & What's Next

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About This Class

Description of class Journal #02: In this follow-up class we will learn the basics of Four & Eightfold symmetries by creating Geometric Building diagrams that will be used as templates to create more advanced designs later on in Class: Journal #03. 

It is highly recommended to watch Journal #01 first before starting this class. Good luck!

Meet Your Teacher

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Dearing Wang

I grew up with a pen in my hand.


Hello, I'm Dearing. I grew up with a pen in my hand. No wallpaper in my parents house was safe. Luckily, I also had a deep interest in science and philosophical questions. When I finished my Architectural bachelor degree at the Delft University of Technology I couldn't wait to join the internet revolution and share my passion for Philosophy and Geometric Art.

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1. Introduction of Four & Eightfold symmetries: Hello and welcome to journals number two. In this course, we are going to be focusing on the symmetries off the four and 8/4 on this page. The structure will be very similar to what we have done in journals. One, the first row is dedicated to creating the wheel diagrams. We're going to learn to divide the circle in four equal parts and in eight equal parts in the second row, we're going to again start to find the pattern which is generated by using or reusing the radius off the circle contained like we did in Row two off Journals one. And we basically just repositioned it on the specific anchor points and try to find out what would happen. And just by doing these simple steps would already generate a certain type of pattern. And on the third row, we explored the effect off when you have a sir circle container and you want to use a circle half the size of the original server container and then place it on the specific harmonic points and see what happened. That's the whole basic idea in the structure off this page, and it's again organized in such a way that the Left column and the Red Column are in a relationship towards each other. The right column is a multiple off the left column and is a increase off double the frequency off the left side. So having said that, that's the whole idea. And once we've done that, we can move on to actually combining these geometric blocks into more advanced patents. So get your tools ready and let's get started. 2. How to Build a Four fold Diagram | Diagram #01: in the coming two lessons, we will build two diagrams that form the basis of the four in the eighth hole Symmetry. In other words, I will demonstrate the basic method off, dividing a circle into four equal parts and into eight equal parts, and to demonstrate how to divide in circling for equal parts. I will use a separate sketch bat instead of the journal sketchbook through drawn, so let's begin. First, we're going to start withdrawing a circle. The size of the circle should allow for enough space above and below the circle on your canvas or paper and then draw a vertical line going through the middle. The imprecise and wrong way would be to try to draw a horizontal line by estimating a rights 90 degree angle perpendicular to the vertical line. The precise way is to use curves and intersections to guide the drawing off straight lines . Let's mark two points where the vertical line into sex with the circle. Then I'm going to grab my compass and anchored in Edo on the South Point and expand the radius. Still, the lead point touches the North Point, and next I draw in semicircle with these points fixed. I also do this on the opposite side. I fixed the needle of the compass on the north Point and draw a semicircle again, extending the radius. Still, it touches the south point and then I draw a semi circle. I'm gonna mark the to anchor points that arise from these two semi circles intersecting on both sides. Then I use my straight edge to connect these two points with a straight line. This land will pass through the circle edge on two points. I will mark thes two points as well. I clean up all the guidelines and points and only keep the central circle with subdivisions . And now we have a circle divided in four equal parts with four anchor points. So to recap what we learned we started with a circle and we used a straight edge to draw a vertical land through the center. Then we grab our compass, replaced the needle point anchoring. It's both on the north side and on the south side, making two semi circles. Then we connected the intersection points outside of the circle, and the straight line passed through the circle container and where the two points meth was the third and 1/4 point, and to get away the North and the South Point formed a four point symmetry on the circle container. 3. How to Build an Eight Fold Diagram | Diagram #02: in the previous video, you already learned to build the four full diagram by learning how to divide the circle into four equal parts. And this four full diagram will function as the starting point for creating the faithful diagram in this video. So make sure that you already have the circle divided into four equal parts before you start drawing. So let's begin. Grab your compass and measure the distance from mid point to the north points using your during compass, then draw two curves outside of the circle on both sides. You can also just make the swing, make a continuous line and erase the part inside of the circle. Later on, we are going to use and reuse this distance to draw the curves in all four wind directions , meaning by placing the needle point on all four wind directions and repeat the previous steps on the South Point, the West Point and the East Point. So the order itself is not so important. Just make sure that you are very process in drawing the curves outside of the circle. We now have a shape with four ear shaped flaps. I'm going to label the corners a B C D. So meaning the corners are the intersections where the two curves meat. Then grab your straight edge and connect point a weak point C with a straight line and do the same thing with the points. B and e connect those two points with a straight line to recap you started with four points on the circle. You have now added four additional points on the circle, and the distance between those points is exactly the same. And together they divide the circle eight equal parts. In the coming videos, we are going to build upon this eighth full diagram. This diagram is going to be very useful to guide all the setups for other kinds off designs based on this symmetry. 4. Adding 4 fold & 8 fold diagrams to our Sketchbook: In the previous video, you learned to build the four in the eighth hole diagram, and we learned to divide the circling to foreign eight. Equal parts. Thes diagrams will function as the fundament on which our designs on this page will be based on. And in this video. I'm going to speed up the video and go through the drawing process quickly because I've already covered the topic off preparing your page, for instance, creating the layout and entering the circle containers and creating sections on the page. But I will come to know the actions that I'm taking. While I add these two diagrams into my journal, we covered the topic off how to organize and set up the layout off the page, and I will do this again, starting with my new blank page. I'm using the template cutouts to measure the distance between the square sections and and marking the boundaries before I connect the markings. After the six sections are laid out on the page, we'll add the circle containers I'm maintaining. The radius of the circle contain a toe 4.5 centimeters for all designs on a page, just like on the previous one and then at all six circle containers and have to find the center off each section. And and I'm doing that by adding across hair and then cleaning up the lines within the circle containers after I've done that, and only leave a small point off the center to find it later on. The first diagram is the forceful diagram that I'm going to add, and I will use the method to divide the circuit in four parts, as we've learned in the previous video. In the second diagram, I'm reusing the distance from the first diagram and have also added the construction diagrams of the eighth Fault method on the left page toe. Help with determining the symmetry of the eight symmetry points on the circle. So grab your compass and measured the distance in between two radios and then transfer that distance onto the diagram of the eighth ful diagram on the page. I'm also using the cardinal rose points that is the North South, the East and West Point, as anchors and a mark the points on the circle with the lead point, - and after that I connect all the points with straight lines going through the center. And finally I add some styling and finish it off by adding some small four millimeter circles on the anchor points and styling them with some red and I also at some shading to the edges off the contained Cirque on the inside. 5. Four Snubbed Leafs | Diagram #9: now that we have practiced creating the diagrams in the previous video, we can expand on this by ending some simple features through the diagrams. And in this video, I want to create a very simple design, nothing fancy. So let's start. I will start with my design on the Left column with a four full diagram that I've prepared , and I'm going to simply at four curves to the diagram and style them with three colors later on. The size of the curve, is defined by the same radius as the radius off the circle container. Then transfer the compass and anchor the needle one off the cardinal points. In my case, I'm placing the needle on the West Point. Make a turn, which your compass and draw a curve inside the circle. Then move your compass and place the needle on the opposite side on the East Point and again crater curve. Then repeat the steps both on the north and the South Point. Now, basically, the design is done, and the next step is to trace all the lines with some ink and add some colors. And by the way, I've adjusted the curves a little bit. by extending them till they intersect. Just to demonstrate how that would look and in later videos won't I will include those minor adjustments in other designs. Now I'm going to just change the mechanical pen inside a pen holder with my 0.5 millimeter fine liner and trace the circle containers both the circle container and the curves inside the circle. And once that is done, I will also use the pen and straight edge to trace the vertical and the horizontal line. But the reason is not so much the aesthetics. Rather, it reminds me off where to place the needle of the compass next time for ah, for me to recreate this design and those vertical lines. And those anchor circles will just emphasize to me where to put put the year needle of the compass, otherwise have to figure it out on my own the next time. So once I'm done, the only thing left to do is to add some color. I will invite you to choose your own colors to create some variation of this. If you would like to, and once I'm done, I'll move on to design number 10 6. Eight Snubbed Leafs | Diagram #10 : In the previous lesson, we built a design using four curves. In this lesson, our increase the complexity a little bit by implying the same size curves onto a 84 diagram instead of a four full diagram, and I will start my design on the right column. This time I will start by creating a circle container, and I'm gonna add a fourfold diagram. Then I have to find the remaining anchor points that are in between the cardinal points, and I do that by measuring the distance on the template on the left page using my compass. I'm going to speed up the process because I've because I've gone through this method already. So I just wanted to, ah, speed the video up a little bit and get things going. And once my a full diagram said, I can start adding the eight curves on the diagram, the size of the curve will be exactly the same size as in the previous video, which was defined by the same radius as the Cirque container. If the compass has changed, then you need to readjust the setting of the compass as before. You do that by placing the needle off accomplished on the center of the circle container and then extend the other leg till it touches the edge of the circle. The steps are technically the same as in the prior video. The difference is that we now have eight anchor points on the circle instead of four. They are evenly spread out over the circle, and we need to place the needle of the compass on each anchor point and make a curve inside a container. Once that is done, the drawing is taking lead them. So the only thing remaining is to style it, and we've been doing that all along. That means tracing the lines that we have drawn with some ink and adding some color of your choice, and after that we can move on to the next drawing. 7. Alternative Method of Eightfold diagram: the designs in this role will be built on top of the eighth full diagram, and I want to show an alternative method off constructing the four and a full diagram with faster results. Downside is that it requires a rotering triangle like the one I'm using, or some other ruler with pre made markings on them, which is spread transparent. It should recognize these from math class because they are widely used in schools. So let's begin. Step one is to draw a vertical line again right through the center of the circle container , then grab your triangular ruler and aligned the triangle along the vertical lines on your triangle. The easy ways to use the 0.2 center The triangle. There is a vertical line perpendicular to the edge, going down from the zero point. Try to align the vertical line that you have just wrong with the vertical line on the transparent ruler. At the same time, try to align the words on toe edge off your ruler so that it crosses the midpoint off your circle container. And if all is aligned, then draw the horizontal line, and basically the result is a fourfold diagram and you're dumb. And the next thing to do if you want to do a eightfold diagram, is to drop the two diagonal lines in the circle container, and we will be using the 45 degree guidelines on the triangular ruler to do show. And this time we will align both the horizontal as a vertical line with the ruler, so use the zero point as a center. Ah, you notice that there are two lines running from the zero point that are perpendicular to each other. Try to overlay the two lines over the lines that you have drawn, and then go ahead and draw a straight line and make sure that it runs through the centre and repeat that process on the opposite side. If all goes well, you will end up with eight full diagram, and it's much quickly off course and much more convenient, especially if you want to create Ah, large amount off drawings based on these symmetries, and you can quickly get your results. But it wasn't important to first demonstrate to you the more traditional method the classical way off, dividing without any fancy stuff and only keep in mind using the very basic principles off finding the vertical lines and the horizontal lines in the perpendicular angles, etcetera. Um, and now that we have gone through those methods, it's also nice to know, of course, the more quicker, easier way to do things. So you have both options and it's up to you to the side which method you want to use. So let's move on to creating some designs now that we can apply these techniques. 8. Four circles | Diagram #11 : In the previous lessons, we built design number nine and 10 using curves with the radius equal to the size off the radius of the circle container. In the next warring, I'm going to change a few simple settings compared to the previous two designs. The ingredient that I want to using the design is a circle half the size off the show container. I want the circle to fit right in between the centre and the edge off the circle container , and that's going to be my building element. Let's see how changing this one variable as Bella's, how the positioning off the element will affect the overall look off the pattern. But first I have to find the exact midpoint between these two extremes. So the question is, where is the midway point? So let's start with the eight fault diagram as a base diagram. Let's mark a few points on the diagram. They are the North, the East and the South Point. Then we connect the's points, and what happens is thes lines were intersected diagonals off the eighth false diagram. Now the points where these lines intersect, mark these points, then connect these two points and when you have a vertical line that intersects the words on the whole line. That's the point where the middle point is. Grab your compass and place the needle point on the center and extend the radius till the midway point, then mark all four intersections with a point. So where the circle meets the vertical and the horizontal axes, then clean up all excess lines and only keep the mid points grabbed, accomplish and draw a circle with the anchor points on one of the mid points like below. So essentially you have four mid points, each for located on each side, off the X and the Y axis, as we would would call it in mathematics, for example. So repeat this step off, creating a circle, using the anchor point on the remaining three points and essentially one. Just once you've done that, we are done, and our pattern is essentially complete now, as you are used to it. By now, we only need to ah, style eyes a little bit and put a little bit of emphasis on the anchor points by using the template to create small circles just to emphasize that these points are important for the mid points and where to put the anchor points of the compass. And once you've done that, we add some in clients to emphasize the lines. - And as always, I add some color. I'm using some red and some green, and I'm also keeping the middle circle made a little mistake by over running part of the drawing, which I didn't want to show, had to correct that. But I have actually five circles instead of four. But the principle of the idea is more important about Saudis. Four circles can be contained within the larger sir container, and the fifth circle at the Centre is Mawr to emphasize the anchor points that that makes it possible to locate those anchor points. So I decided to leave that Circo in place as well. So essentially, we're done. Once we've done all the tracing and all the coloring, and we can move on to the next drawing where we will increase the frequency 9. Eight circles | Diagram #12 : So in the previous video, we created a design using a building element, which was the half size off the circle container. The first challenge was to find a way to determine the exact midpoint between the centre and the edge of the circle container, and I use the faithful template as the basis off the design, and what I did was I first made a connection between the cardinal points with straight lines, and these straight lines would then intersect with the. These lines would then intersect with the diagonals, which I then marked with a anchor point and then connected the two points with a straight line and marked the point where it intersected with the horizontal line. And that specific point, um, marked the midpoint between the two extremes. And it was exactly halfway between the edge of the circle and the center of the circle, and I continued then to draw a circle anchored at the center, where the edge passed through the anchor point and this circle was half the size of the circle container. This circle would run through all the axes, so the vertical and the horizontal axes and these points were then marked. So the smaller circle functions as a visual guide, and it helps to determine all the intersections while passing through all the straight lines. So the vertical line and the diagonal lines in the horizontal lines. And there are eight intersection points. These intersections, which have marked than, um, the anchor points on which the needle off the compass are anchored on so that you can make a rotation with your compass and thus have a circle created. And when you do that eight times around the middle of the container, you end up with a design, which has eight circle circling around the center technically and structurally. Then it's already done, and the next step is to, ah, style eyes. It's trace it with some ink and adding some color, as I've been doing in all the previous lessons, and by then l speed up this video and we can move on to the next part of the course 10. Recap & What's Next: we have come to the end off journals to, and we now have 12 diagrams in total. We can already say we have quite a few of building blocks to work with, and in general three will start to combine some of these building blocks and to be precise , will be using building blocks number three and number five. And that's our next project. So see you in the next course.