Today we will talk about a phenomenon that each of us constantly encounter in life: about symmetry. What is symmetry?
Approximately we all understand the meaning of this term. The dictionary says: symmetry is the proportionality and full correspondence of the arrangement of parts of something relative to a line or point. There are two types of symmetry: axial and radial. Let's look at the axis first. This is, let's say, "mirror" symmetry, when one half of the object is completely identical to the second, but repeats it as a reflection. Look at the halves of the sheet. They are mirror symmetrical. The halves of the human body (full face) are also symmetrical - the same arms and legs, identical eyes. But let's not be mistaken, in fact, in the organic (living) world, absolute symmetry cannot be found! The halves of the sheet do not copy each other perfectly, the same applies to human body(take a look yourself); the same is true of other organisms! By the way, it is worth adding that any symmetrical body is symmetrical relative to the viewer in only one position. It is necessary, say, to turn the sheet, or raise one hand, and what? - see for yourself.
People achieve true symmetry in the products of their labor (things) - clothes, cars ... In nature, it is characteristic of inorganic formations, for example, crystals.
But let's move on to practice. It’s not worth starting with complex objects like people and animals, let’s try to finish the mirror half of the sheet as the first exercise in a new field.
Draw a symmetrical object - lesson 1
Let's try to make it as similar as possible. To do this, we will literally build our soul mate. Do not think that it is so easy, especially the first time, to draw a mirror-corresponding line with one stroke!
Let's mark a few reference points for the future symmetrical line. We act like this: we draw with a pencil without pressure several perpendiculars to the axis of symmetry - the middle vein of the sheet. Four or five is enough. And on these perpendiculars we measure to the right the same distance as on the left half to the line of the edge of the leaf. I advise you to use the ruler, do not really rely on the eye. As a rule, we tend to reduce the drawing - it has been noticed in experience. We do not recommend measuring distances with your fingers: the error is too large.
Connect the resulting points with a pencil line:
Now we look meticulously - are the halves really the same. If everything is correct, we will circle it with a felt-tip pen, clarify our line:
The poplar leaf has been completed, now you can swing at the oak one.
Let's draw a symmetrical figure - lesson 2
In this case, the difficulty lies in the fact that the veins are marked and they are not perpendicular to the axis of symmetry, and not only the dimensions but also the angle of inclination will have to be exactly observed. Well, let's train the eye:
So a symmetrical oak leaf was drawn, or rather, we built it according to all the rules:
How to draw a symmetrical object - lesson 3
And we will fix the topic - we will finish drawing a symmetrical leaf of lilac.
He also has an interesting shape - heart-shaped and with ears at the base you have to puff:
Here is what they drew:
Look at the resulting work from a distance and evaluate how accurately we managed to convey the required similarity. Here's a tip for you: look at your image in the mirror, and it will tell you if there are any mistakes. Another way: bend the image exactly along the axis (we have already learned how to bend correctly) and cut the leaf along the original line. Look at the figure itself and at the cut paper.
If you think for a minute and imagine any object in your imagination, then in 99% of cases the figure that comes to mind will be correct form. Only 1% of people, or rather their imagination, will draw an intricate object that looks completely wrong or disproportionate. This is rather an exception to the rule and refers to unconventionally thinking individuals with a special view of things. But returning to the absolute majority, it is worth saying that a significant proportion of the correct items still prevail. IN article will go speech exclusively about them, namely about the symmetrical drawing of those.
Image of the right subjects: just a few steps to the finished drawing
Before you start drawing symmetrical object, you need to select it. In our version, it will be a vase, but even if it does not in any way resemble what you decided to depict, do not despair: all the steps are absolutely identical. Follow the sequence and you'll be fine:
- All regularly shaped objects have a so-called central axis, which, when drawing symmetrically, should definitely be highlighted. To do this, you can even use a ruler and draw a straight line in the center of the album sheet.
- Next, carefully look at your chosen object and try to transfer its proportions to a piece of paper. It is not difficult to do this if, on both sides of the line drawn in advance, outline light strokes, which will subsequently become the outlines of the object being drawn. In the case of a vase, it is necessary to highlight the neck, bottom and the widest part of the body.
- Do not forget that symmetrical drawing does not tolerate inaccuracies, so if there are some doubts about the intended strokes, or you are not sure about the correctness of your own eye, double-check the pending distances with a ruler.
- The last step is to connect all the lines together.
Symmetric drawing available to computer users
Due to the fact that most of the objects around us have correct proportions, in other words, are symmetrical, computer application developers have created programs in which absolutely everything can be easily drawn. Just download and enjoy creative process. However, remember, the machine will never be a substitute for a sharpened pencil and album sheet.
For centuries, symmetry has remained a subject that fascinates philosophers, astronomers, mathematicians, artists, architects and physicists. The ancient Greeks were completely obsessed with it - and even today we tend to see symmetry in everything from furniture arrangement to hair cutting.
Just keep in mind that once you realize this, you are likely to have an overwhelming urge to look for symmetry in everything you see.
(Total 10 photos)
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1. Romanesco broccoli
Perhaps when you saw Romanesco broccoli in the store, you thought it was another example of a genetically modified product. But in fact, this is another example of the fractal symmetry of nature. Each broccoli inflorescence has a logarithmic spiral pattern. Romanesco is similar in appearance to broccoli, but in taste and texture - cauliflower. It is rich in carotenoids, as well as vitamins C and K, which makes it not only beautiful, but also healthy food.
For thousands of years, people have marveled at the perfect hexagonal shape of the honeycomb and wondered how bees can instinctively create a shape that humans can only reproduce with a compass and straightedge. How and why do bees have an urge to create hexagons? Mathematicians think that this perfect shape, which allows them to store the maximum possible amount of honey using the minimum amount of wax. In any case, it's all a product of nature, and it's pretty damn impressive.
3. Sunflowers
Sunflowers boast radial symmetry and interesting type symmetry known as the Fibonacci sequence. Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (each number is determined by the sum of the two previous numbers). If we took our time and counted the number of seeds in a sunflower, we would find that the number of spirals grows according to the principles of the Fibonacci sequence. In nature, there are so many plants (including romanesco broccoli) whose petals, seeds and leaves correspond to this sequence, which is why it is so difficult to find a four-leaf clover.
But why do sunflowers and other plants follow mathematical rules? Like the hexagons in the hive, it's all a matter of efficiency.
4 Nautilus Shell
In addition to plants, some animals, such as the Nautilus, follow the Fibonacci sequence. Nautilus shell twists into a "Fibonacci spiral". The shell tries to maintain the same proportional shape, which allows it to maintain it throughout its life (unlike people who change proportions throughout their lives). Not all Nautiluses have a Fibonacci shell, but they all follow a logarithmic spiral.
Before you envy mathematician clams, remember that they do not do this on purpose, it is just that this form is the most rational for them.
5. Animals
Most animals are bilaterally symmetrical, which means they can be split into two identical halves. Even humans have bilateral symmetry, and some scientists believe that human symmetry is the most an important factor, which affects the perception of our beauty. In other words, if you have a one-sided face, then you can only hope that this is compensated by other good qualities.
Some reach complete symmetry in an effort to attract a partner, such as a peacock. Darwin was positively annoyed by this bird, and wrote in a letter that "The sight of the peacock's tail feathers, whenever I look at it, makes me sick!" To Darwin, the tail seemed cumbersome and made no evolutionary sense, as it did not fit with his theory of "survival of the fittest". He was furious until he came up with the theory of sexual selection, which claims that animals develop certain features to increase their chances of mating. Therefore, peacocks have various adaptations to attract a partner.
There are about 5,000 types of spiders, and all of them create a near-perfect circular web, with nearly evenly spaced radial support threads and a spiral web to catch prey. Scientists aren't sure why spiders love geometry so much, as tests have shown that a round web won't lure food any better than an irregularly shaped one. The scientists suggest that the radial symmetry evenly distributes the force of impact when the victim is caught in the net, resulting in fewer breaks.
Give a couple of tricksters a board, mowers, and saving darkness, and you will see that people also create symmetrical shapes. Due to the complexity of the design and incredible symmetry of crop circles, even after the creators of the circles confessed and demonstrated their skills, many people still believe that space aliens did it.
As the circles become more complex, their artificial origin becomes more and more clear. It is illogical to assume that the aliens will make their messages more and more difficult when we have not been able to decipher even the first of them.
Regardless of how they came about, crop circles are a pleasure to look at, mainly because their geometry is impressive.
Even such tiny formations as snowflakes are governed by the laws of symmetry, since most snowflakes have hexagonal symmetry. This is partly due to the way water molecules line up when they solidify (crystallize). Water molecules solidify by forming weak hydrogen bonds as they align in an ordered arrangement that balances the forces of attraction and repulsion to form the snowflake's hexagonal shape. But at the same time, each snowflake is symmetrical, but no snowflake is alike. This is because as each snowflake falls from the sky, it experiences unique atmospheric conditions, which cause her crystals to be arranged in a certain way.
9. Milky Way Galaxy
As we have seen, symmetry and mathematical models exist almost everywhere, but are these laws of nature limited to our planet? Obviously not. Recently discovered a new section at the edge of the Galaxy Milky Way, and astronomers believe that the galaxy is a near-perfect mirror reflection myself.
10. Symmetry of the Sun-Moon
Considering that the Sun is 1.4 million km in diameter and the Moon is 3474 km, it seems almost impossible that the Moon can block sunlight and provide us with about five solar eclipses every two years. How does it work? Coincidentally, along with the fact that the Sun is about 400 times wider than the Moon, the Sun is also 400 times further away. Symmetry ensures that the Sun and Moon are the same size when viewed from Earth, and so the Moon can cover the Sun. Of course, the distance from the Earth to the Sun can increase, so sometimes we see annular and not total eclipses. But every one or two years, a fine alignment occurs, and we witness the exciting events known as the complete solar eclipse. Astronomers don't know how common this symmetry is among other planets, but they think it's pretty rare. However, we should not assume that we are special, as this is all a matter of chance. For example, every year the Moon moves away from the Earth by about 4 cm, which means that billions of years ago, every solar eclipse would have been a total eclipse. If things continue like this, then total eclipses will eventually disappear, and this will be accompanied by the disappearance of annular eclipses. It turns out that we are just in right place V right time to see this phenomenon.
In this lesson on Adobe Illustrator we will draw a circular ornament, just such an inflated mandala. It is assembled from a fragment of a pattern, reproduced in a circle with reflection. Also, this pattern goes along the inner circle of the mandala with an offset relative to the outer one. Although such a construction seems complicated at first glance, a mandala is made in illustrator quickly and easily. All thanks to templates for mirror drawing Live Mirror Illustrator Templates that we will be using in the tutorial.
Live Mirror Templates are 27 mirror drawing templates in illustrator. Templates do not need to be installed, just open them in Adobe Illustrator and draw. There are many rotation, duplication and striping effects available, all of which can be easily expanded for stocks.
Possibilities Live Templates Mirror Templates can be seen in this video.
Buy a set of 27 Live Mirror Templates at MAI Tools for a micro price of just $9 - Live Mirror Illustrator Templates
So, when the magic templates arrive on your computer, you can safely proceed to the lesson.
Creating a circular pattern
Unzip the templates Live Mirror. Inside you will find AIT files mirror patterns and their preview in PNG format. Take template number 26 . From the preview, you can see that this is a two-level template, where reflection, rotation and alternation of the working sector are applied.
Opening the template file in illustrator (File > Open > Live-Mirror-Template-26.ait). A new document appears that looks like this.
To see where the drawing sector is, click Ctrl+Y (View > Outline).
Illustrator will change the preview view and you will see only one caption Draw some cool designs here. It is there that the working sector is located, it is indicated in red in the screenshot. In this sector, you will need to draw our future ornament. The remaining sectors will be filled automatically with reflected copies.
Delete the text from the working sector, select it and click Delete on keyboard. To return to normal mode, press ctrl+y again. Now you can draw in this sector. Use any tool for this.
I decided to take a brush-blot Blob Brush Tool (Shift+B), and drew a few ornamental elements along the vertical guide that bounds the working sector. At the same time, I drew only half of the pattern on the left, it is highlighted in the screenshot. All other copies appear automatically during the drawing process. It is very convenient, you can immediately see what happens. By the way, Blob Brush Tool (Shift+B) especially useful when working with a graphics tablet. You can look at this topic cast: How to draw with a graphics tablet in Adobe Illustrator.
We continue to draw in the working sector. I decided to add smaller details on the left side of the working sector. To change settings Blob Brush Tool, reduce the line thickness, etc., just double-click on the tool icon. Thus, we sketch all the space in the sector. You can go down the guide that limits the sector from below to make the pattern continuous.
Just a few minutes, and the ornament is ready.
Working with color
The ornament can already be expanded and finished somehow further in colors using the method familiar to you. But you can work with color in reflection pattern mode as well. For example, let's change the color of the outlines. For this we take magic wand Magic Wand Tool (Y), and click on any part of the ornament in the working sector.
The illustrator will select vector objects drawn by hand, because we have them all in the same color. Now you can assign them a different color. I chose blue.
Forms for pouring can be drawn with the same blot brush. But to do this, you must first enable the function Draw Behind- drawing behind objects. To do this, press on the keyboard Shift+D once (to switch to normal drawing mode, you need to deselect through Shift+Ctrl+A and then press again Shift+D). Then take a blot brush Blob Brush Tool (Shift+B), make the line thicker, choose a different color, and just paint over the elements of the ornament as in the coloring book.
We paint over from above in the working sector, and the objects will appear from below, as it should be filled. All thanks to the function Draw Behind. In this case, it is not necessary to ensure that the colored forms are strictly inside the contours. If spades or inaccuracies appear, this gives the drawing liveliness.
We color the entire working sector in this way. In other sectors, the fill will appear automatically.
Preparation and preservation
When everything is ready, you need to select the entire template along with the content, this can be done through Ctrl+A. Then execute the command Object > Expand Appearance.
