Publications  NAZCA LINES 02.08.2011. GEOGLYPH «ESTRELLA»




Colour is life and the world without paints is represented to us dead. Colours are primary concepts, children of first-born, colourless light and its contrast colourless darkness. As the flame generates light so light generates colour. Colour is a child of light and light is his mother. Light as the first step in world creation, opens to us through colour its live soul. Nothing could so to amaze human mind, as occurrence in heavens of a huge colour wreath.

(Iohannes Itten)

 Not so long ago in rocky areas of place Palpa in Peru in the neighborhood with known area of desert Naska has been found out geoglif on local dialect named "Estrella" ("Star"). The geoglif really unusual. It is distinguished with prevalence of the geometrical figures collected in uniform easily readable geometrical composition. It settles down on rather even platform, an order of kilometer in length, in rocky district, with a difficult relief, with co-ordinates 14°38’ 40”a southern latitude and 75°10 ’ 17” the western longitude.


Geoglif from the height of the bird's flight. Photo Eduardo Herran 

The analysis of components geoglif shows that it is not simply decorative drawing. In the composition there are the laws, saying that elements used in it have informative character and their arrangement in drawing confirms that they are not casual. Semantic signs of elements say about pithiness and illustrativity of images about that the geoglif is intended for perusal. Besides, these laws develop in the certain rules setting logic directions, some vectors in which direction, according to these rules, the composition can develop further.

The given image is already for a long time a subject of steadfast attention of various scientists and researchers. Their interest is quite proved: first, the drawing has ideal geometrical proportions, creation of which is absolutely impossible without developed correct system of co-ordinates and knowledge of geometry laws, secondly the unique techniques of execution which has become theoretically possible for us only last fifty years, and the drawing as it is known has not less than 1000 age! Also it is rather probable that in the drawing there is a ciphered information, the key to which opening consists in lengths, sizes and other parities of the given drawing.


Geoglif "Estrella".

Just from proportional parities of sizes we will try to examine the given drawing. But, at first, some words are necessary to tell about properties of colour.

  In the Internet there is a remarkable book Iohannes Itten «BASES OF COLOUR». It has suggested an idea that possibly «Estrella» is connected with colour constructions and is very similar to the scheme of construction of modern colour palettes, for example palettes RGB. In the book principles of harmonious combination of colours, their properties and the characteristic are described in detail. Here are some citations from the book, concerning properties of colour and specificity of its perception with eye of the person.

 «… In order to avoid mess in further acquaintance in the book I would like to give more exact definition of concept" character of colour "and" tone of colour ". Speaking about character of any colour, I mean its position or a place in a colour circle or in a colour sphere. As pure, not blacked out colours also all mixes with other colours possess clearly expressed character. So, for example, green colour can be mixed with yellow, orange, red, violet, dark blue, white and black colour, and in each case it gets specific, unique character. Each change of colour as a result of simultaneous influences also creates new, its special character. When we wish to define degree of clarity or darkness of any colour we speak about its voice-frequency quality, or"валёре". Tone of colour can be changed in two ways: or through connection of the given colour with white, black or grey, or by mixture it with two colours of various clarity.


In 1676 sir Isaak Newton by means of a trihedral prism has decomposed white sunlight into a colour spectrum. The similar spectrum contained all colours except for the purple. Newton carried out the experiment as follows (fig. 1): the Sunlight was passed through a narrow crack and fell on a prism. In a prism the beam of white colour stratified in separate spectral colours. Stratified thus it directed then to the screen where a spectrum image appeared. The continuous colour tape began with red colour and through orange, yellow, green, dark blue came to the end with violet. If this image then was passed through collecting lens connection of all colours gave again white colour. These colours turn out from a solar beam by means of refraction. There are also other physical ways of formation, for example, connected with processes of interferences, diffractions, polarization and fluorescence. If we divide the spectrum in two parts, for example red-orange-yellow and green-blue-violet, and collect each of these groups with a special lens as a result we will receive two mixed colours which mix, in turn, also wil give us white colour. Two colours, which association gives white colour, are called as complementary colours. If we remove one colour from a spectrum, for example, green, and by means of a lens we will collect the remained colours - red, orange, yellow, dark blue and violet, the mixed colour received by us will appear as red, that is with colour additional in relation to removed by us green one. If we remove yellow colour, the remained colours - red, orange, green, dark blue and violet will give us violet colour that is colour, additional to the yellow. Each colour is additional in relation to a mix of all other colours of a spectrum. In the mixed colour we cannot see its separate components. In this respect the eye differs from a musical ear which can separate from any of chord sounds. Various colours are created with light waves which represent a certain sort of electromagnetic energy.
The human eye can perceive light only at length of waves from 400 to 700 mill micron: 1 micron or 1 m = 1/1000 mm = 1/1 000000 m. 1 mill micron or 1 MIT) =1/1 000 000 mm.

The length of waves corresponding to separate colours of a spectrum, and corresponding frequencies (number of fluctuations in a second) for each prismatic colour has following characteristics: relation of frequencies of red and violet colour approximately is equal to 1:2 that is the same as in musical octave. Each colour of a spectrum is characterized with its length of wave that is it can be absolutely precisely set with length of a wave or frequency of fluctuations. Light waves have no colour themselves. Colour appears only in perception of these waves with a human eye and brain. How he distinguishes these waves till now is not known completely. We only know, that various colours appear as result from quantitative distinctions of a photosensitivity. It is necessary to investigate the important question about body colour of subjects. If we, for example, put a filter passing red colour, and a filter passing green, before an arc lamp both filters together will give black colour or darkness. Red colour absorbs all beams of a spectrum, except beams in that interval which corresponds to red colour, and the green filter detains all colours, except the green. Thus, any beam is not passed, and we receive darkness. Colours absorbed in physical experiment are called also as subtracted. Colour of subjects appears, mainly, in the process of wave’s absorption. The red vessel looks red because it absorbs all other colours of a light beam and reflects only the red. When we speak: «This cup red "we actually mean that the molecular structure of a cup surface is such that it absorbs all light beams, except the red. The cup itself has no any colour; colour is created during its illumination. If a red paper (the surface absorbing all beams except red) is shined with green light the paper will seem to us black because green colour does not contain the beams corresponding to red colour which could be reflected with our paper. All picturesque paints are pigmentary or material. These are absorptive (absorbing) paints, and in time their mixing it is necessary to be guided with subtraction rules. When additional paints or the combinations containing three primary colours yellow, red and dark blue are mixed up in a certain proportion result will be black while the similar mix of the immaterial colours received in Newton's experiment with a prism gives as a result white colour because here association of colours is based on an addition principle, instead of subtraction.

Colour and colour influence.

Colour vision appearing in eyes and consciousness of a person, bears in itself the human semantic maintenance. However, in piques of an eye and brain can come to accurate distinction of colour only by means of comparisons and contrasts. Meaning and value of chromatic colour can be defined only by means of its relation to any achromatic colour black, white or grey, or to its relation to one or several other chromatic colours. The perception of colour, in contrast to its physical and chemical reality, is a reality psychophysiological.

Colour harmony.

The concept of colour harmony should be withdrawn from area of subjective feelings and transferred to area of objective laws. Harmony is balance, symmetry of forces. Studying of the physiological party of colour vision approaches us to the decision of this problem. So, if some time to look at a green square, and then close eyes, in our eyes we will have a red square. And on the contrary, observing a red square, we will receive its "inversion» green. These experiences can be made with all colours, and they confirm, that the colour image appearing in eyes, is always based on colour, additional to really seen. Eyes demand or generate complementary colours. And it is need of nature to reach balance. It is possible to name this phenomenon consecutive contrast.

GEOGLYPH «ESTRELLA»An other experience consists in that on a colour square we impose a grey one of the smaller size, but the same brightness. On yellow this grey square will seem to us light-violet, on orange - bluish-grey, on red -greenish -grey, on green - redish-grey, on dark blue – orange -grey and on violet - yellow-grey (fig. 31-36). Each colour forces grey to accept its additional shade. Pure colours also tend to paint other chromatic colours in the complementary colour. This phenomenon is called as simultaneous contrast. Consecutive and simultaneous contrasts point to that the eye receives satisfaction and sensation of balance only on the basis of the law about complementary colours. We will examine it also on the other hand. Physicist Rumford the first has published in 1797 in Nikolson-journal his hypothesis that colours are harmonious in that case if their mix gives white colour. As the physicist he started from studying of spectral colours. In the section devoted to physicist of colour it was already said, that if to withdraw any spectral colour, for example, red, from a colour spectrum, and other painted light beams yellow, orange, violet, dark blue and green to collect by means of a lens together the sum of these residual colours will be green, that is we will receive colour additional to the withdrawn. In area of physics the colour mixed with the complementary colour, forms a total sum of all colours, that is white colour, and the pigmentary mix will give in this case grey-black tone. The following remark belong to Physiologist Evaldu Goering " To average or neutral grey colour corresponds that condition of an optical substance in which dissimilation, the expense of the forces spent for perception of colour, and assimilation - their restoration are counterbalanced. It means, that average grey colour creates in eyes a balance condition ". Goering has proved, that average grey is required to an eye and a brain, otherwise, in its absence, they lose calmness. If we see a white square on a black phon, and then we will look at an other side in the form of the residual image we see a black square. If we look at a black square on a white phon the residual image will appear white. We observe in eyes aspiration to restoration of balance condition. But if we look at a medial-grey square on a medial-grey phon in eyes there will be no any residual image differing from medial-grey colour. It means, that medial-grey colour corresponds to the balance condition necessary for our sight. The processes going in visual perception, cause corresponding mental sensations. In this case harmony in our visual device testifies about psychophysical condition of balance in which dissimilation and assimilation of a visual substance are identical. The neutral grey corresponds to this condition. I can receive the same grey colour from black and white or from two complementary colours in that case if their structure includes three primary colours yellow, red and dark blue in an appropriate proportion. In particular, each pair of complementary colours includes all three primary colours: red - green = red - (yellow and dark blue); dark blue - orange = dark blue - (yellow and red); yellow - violet = yellow - (red and dark blue). Thus, it is possible to tell, that if the group of two or more colours contains yellow, red and dark blue in corresponding proportions the mix of these colours will be gray. Yellow, red and dark blue represent the general colour totality. For its satisfaction this general colour sheaf is required to an eye, and only in this case the perception of colour reaches harmonious balance. Two or more colours are harmonious if their mix represents neutral grey colour. All other colour combinations which do not give us grey colour, on their character become expressional or disharmonious.

The main principle of harmony starts from the law of complementary colours caused by physiology. In his work about colour Goethe wrote about harmony and integrity so: "When an eye beholds colour, it comes, at once, to active condition and by its nature inevitably and unconsciously immediately creates other colour which in connection with the given colour comprises all colour circle. Each separate colour, thanks to specificity of perception forces an eye to aspire to generality. And then, to achieve it, the eye, in purposes of self-satisfaction, searches nearby with each colour of any colourless-empty space to which it could produce missing colour. In this the main rule of colour harmony is shown.

Appears a question what defines this impression? It is possible to answer, that those colours between which there is a natural communication, i.e. an order are pleasant. Combinations of colours, the impression from which is pleasant to us we name harmonious. So the main law, it would be possible to formulate so: Harmony = the Order. To define all possible harmonious combinations, it is necessary to find the system of an order providing all their variants. The orders are easier the more obvious will be self-evident harmony. We have found basically two systems, capable to provide this order: the colour circles connecting colours, possessing identical degree of brightness or blackouts and triangles for the colours representing mixes of this or that colour with white or black. Colour circles allow defining harmonious combinations of various colours, triangles harmony of colours of equivalent colour tonality ".

Extremely important basis of any aesthetic theory of colour is the colour circle as it gives system of colours arrangement. It means, that opposite colours should be additional, i.e. giving at mixing greying colour. So, in my colour circle dark blue colour stands against orange, and the mix of these colours gives us grey colour. Harmony definition pawns the base of harmonious colour composition. For last is rather important quantitative relation of colours. On the basis of brightness of main colours Goethe has deduced the following formula of their quantitative parity: yellow: red: dark blue = 3: 6: 8. It is possible to make the general conclusion that all pairs of the complementary colours, all combinations of three colours in 12-parts colour circle which are connected with each other through equipotential or isosceles triangles, squares and rectangles, are harmonious.

GEOGLYPH «ESTRELLA»Yellow-red-dark blue forms here the basic harmonious triad. If these colours in a system 12-parts colour circle connect among themselves we will receive an equipotential triangle. In this triad each colour is presented with limiting force and intensity and each of them acts here in typically patrimonial qualities, that is yellow operates on the spectator as yellow, red , as red and dark blue , as dark blue. The eye does not demand additional complementary colours and their mix gives dark black-grey colour. Yellow, red-violet and blue-violet colours are united with a figure of an isosceles triangle. Harmonious accord of yellow, red-orange, violet and blue-green are united with a square. The rectangle gives a harmonious combination yellow-orange, red-violet, blue-violet and yellow-green. The sheaf of geometrical figures consisting of equipotential and isosceles triangle, square and rectangle, can be placed in any point of colour circle. These figures can be rotated within a circle, replacing, thus, triangle consisting from yellow, red and dark blue, with triangle, uniting yellow-orange, red-violet and blue-green or red-orange, blue-violet and yellow-green. The same experiment can be carried out with other geometrical figures. The further development of this theme can be found in the section devoted to harmony of colour accords.

12-parts colour circle.

For introduction in system of colour designing we will create 12-parts colour circle, leaning on main colours, yellow, red and dark blue (fig. 3). As it is known, the person with normal sight can define the red colour which does not have neither bluish, nor a yellowish shade; yellow - not having neither bluish, nor reddish tone, and dark blue, not having neither greenish, nor a reddish shade. Thus, studying each colour, it is necessary to examine it on a neutral grey phon. Three main colours of the first order are placed in equipotential triangle so that yellow was at the top, red below on the right and dark blue below on the left. Then the given triangle is entered in a circle and on its basis the equipotential hexagon is built. In the formed isosceles triangles we place three mixed colours, each of which consists of two main colours, and we receive so colours of the second order: yellow + red = orange, yellow + dark blue = green, red + dark blue = the violet.

GEOGLYPH «ESTRELLA»Then at some distance from the first circle we draw another and divide the ring received between them into twelve equal parts, placing the basic and compound colours in a place of their arrangement and leaving thus between each two colours empty sector. Into these empty sectors we enter colours of the third order, each of which is created thanks to a colour mixture of the first and second order and we receive:
Yellow + orange = yellow-orange,
Red + orange = red-orange,
Red + violet = red-violet,
Dark blue + violet = blue-violet,
Dark blue + green = the blue-green
Yellow + green = the yellow-green. Thus, there is a correct colour circle of twelve colours in which each colour has it’s the invariable place and their sequence has the same order as in a rainbow or in a natural spectrum (fig. 3). Isaak Newton has received in his time this closed colour circle in which he has added absent purple colour to spectral colours that has strengthened its general constructability. In our circle all twelve colours have equal pieces, therefore the colours taking diametrically opposite places in the relation to each other, appear additional. This system gives possibility instantly and precisely to imagine yourself all twelve colours and easily to arrange between them all their variations.

Contrast of colour distribution.

Contrast of colour distribution characterizes dimensional relations between two or several colour planes. Its essence is opposition between "many" and «a little ", "big" and "small". Colours can be packed with each other with stains of any size. But we would like to find out what quantitative or spatial relations between two or several colours can be considered counterbalanced and at what conditions any of them will not be will be allocated more than another one. Force of influence of colour is defined with two factors. First, its brightness and, secondly, the size of its colour plane. For this purpose. So that to define brightness or clarity of this or that colour, it is necessary to compare them among themselves on neutral-grey phon of average clarity. Thus we will be convinced that intensity or clarity of different colours is various. Goethe has established simple numerical relations very convenient in our case for this purpose. These relations are approximate.

According to Goethe it is possible to present a light saturation of various colours system of following relations:

The yellow: 9 orange: 8 red: 6 violet: 3 dark blue: 4 green: 6

Let's result relations of clarity following pairs of complementary colours:

The yellow: violet = 9:3 = 3:1 = 3/4; 1/4
The orange: dark blue = 8:4 = 2:1 = 2/3; 1/3
The red: green =6:6=1:1=1/2:1/2

If for harmonization of the sizes of colour planes to operate with these data it is necessary to use equivalents, the return to relations of light sizes. That is, yellow colour, being three times stronger, should occupy only one third of the space occupied with its additional violet colour. As it is shown in drawings for harmonious relations of the planes filled with complementary colours, following proportions are characteristic:

The yellow: violet = 1/4: 3/4
The orange: dark blue - 1/3: 2/3
The red; green = 1/2: 1/2

Thus, the harmonious sizes of planes for the main and additional colours can be expressed following digital relations:

The yellow: 3 orange: 4 red: 6 violet: 9 dark blue: 8 green: 6 or:

The yellow: orange =3:4
The yellow: red =3:6
The yellow: violet =3:9
The yellow: dark blue =3:8
The yellow: the red: dark blue =3:6:8
The orange: the violet: green =4:9:6

In appropriate way it is possible to present as well all other colours in their proportional connection among themselves.

GEOGLYPH «ESTRELLA»In the right drawing the circle of a harmonious relation of main and additional colours in there spatial characteristics is presented. It is constructed as follows:

- At first all circle is shared on three equal parts, then each of them, in turn, again is shared with proportionally numerical relations of two additional colours:
- One third of a circle for yellow and violet colour is shared in the ratio 1/4: 3/4;
- Other third, for orange and dark blue, as 1/3: 2/3,
- And last third for red and green is presented with a relation 1/2; 1/2,

When these proportions are found, another is drawn of the same size circle where in accordance with the found proportions colour number in according to sequence of a colour circle is created: yellow, orange, red, violet, dark blue and green. Harmonious in their sizes colour planes make an impression of calmness and stability. Contrast of colour spreading in this case is neutralized thanks to harmoniously made colour stains.

The system of quantitative relations presented here is valid only in using of colours in their maximum brightness. During of its change vary the corresponding sizes of the colour areas. Both factors brightness and the size of colour plane are the most close connected between them. ""

From all above told we are interested in 12-parts a colour circle and a circle of a harmonious relation of the main and additional colours in their spatial characteristics. We will impose 12-parts colour circle on drawing of Palpa.


Now in a circle we construct some geometrical figures corresponding to harmonious combination of colours and we look, as they co-operate with external circles. At once it is possible to pay attention that almost all points of figures crossing in the circle lay on lines and circles of internal figure geoglif.


Apparently from drawing with points on external circles co-operate both lines of figures and lines geoglif itself.

Now we will construct from geoglif in an external circle a circle of a harmonious combination of colours in their spatial characteristics. 

1. The spatial characteristic of a segment corresponding to orange colour is already set with existing points C and D of geoglif.

2. We will make a line 1 through four internal points and a point A geoglif. Crossing of this line with an external circle, the point B, gives a border of the spatial characteristic of violet and red colours.

3. Having made a vertical line 2 through a point B, parallel to the side of the big square, on crossing with a circle we would receive a border of yellow and green colours.

4. The border of green and dark blue colours is set with an existing line of geoglif passing through point F.

5. Having made a line 3 parallel to the side of the big square, through crossing of a line 1 with an external circle we would receive a point K border of dark blue and violet colours (a line 4).


 So, having made only three lines, we have constructed a circle of harmonious combination of colours in their spatial characteristics. It is interesting also the moment that spatial colours were constructed mirror rather of 12parts colour circles entered in the big square.

 Having made some more lines, as it is shown in drawing it is possible, to receive a relation of gold section, and in two variants.

In the beginning.