{"id":372,"date":"2013-10-23T18:05:50","date_gmt":"2013-10-23T18:05:50","guid":{"rendered":"http:\/\/gigirockproductions.com\/test\/?page_id=372"},"modified":"2013-10-23T18:05:50","modified_gmt":"2013-10-23T18:05:50","slug":"the-six-pointed-star-koch-fractal","status":"publish","type":"page","link":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/articles\/2007-articles\/the-six-pointed-star-koch-fractal\/","title":{"rendered":"The Six Pointed Star – Koch Fractal"},"content":{"rendered":"

\"six_star_1997\"
\nIn July, 1998 the Star Nations sent another Starglyph that was important for all people. It appeared under the white horse of Milk Hill, in Wiltshire, England.\u00a0Mathematically it is referred to as a >Koch Fractal.\u00a0 This glyph had an unusual geometric flower in its center.<\/p>\n

One of the elements I uncovered as I was working on this glyph, became important to its entire understanding.\u00a0 After having worked on it for a length of time, I had a feeling that the inner star or flower may have been an important fractal, not recorded in the text or literature archives of Earth.\u00a0 Could the Star Nation People have sent something that might show a geometric sample yet to be understood here within the framework of our knowledge?<\/p>\n

I knew of a mathematician in Canada who had an extensive understanding of mathematics, and whom I thought might have the knowledge for what I was researching.\u00a0 I asked if he knew of this fractal.\u00a0 He hadn’t seen it and didn’t know.\u00a0 He referred me to a colleague of his in Germany, (a top notch mathematician) who responded to me with a note that explained it was not his field of expertise and he had not seen it before.\u00a0 This left me with only one person who might be able to answer my question, Dr. Benoit Mandelbrot, the world’s foremost authority on fractal geometry.\u00a0 I drafted a note to him in question of this glyph.<\/p>\n

\"fractal1\"<\/p>\n

Some weeks later, I received a reply explaining that he had formulated this inner flower’s geometry, only to discover it had already been discovered in the early 1900’s, by another mathematician.\u00a0 He called it the Inner Infinity<\/p>\n

Dr. Mandelbrot referred me
\n<\/a> to his textbook he had written for university level students.\u00a0 In a grueling search, I found no other reference of this fractal.<\/p>\n

I did discover through my own visionary abilities, that the relationship between the outer outline of the Koch Fractal and the center flower, were geometrically perfect relationships<\/p>\n

The conceiver of this Starglyph had presented in a field, a relationship between this inner flower and outer fractal, which to the best of my research never existed on this planet before, until it appeared in the field. It was my belief the Star Nations had succeed in finding a way that might express something we could understand, but had been beyond our knowledge base to present, in a very beautiful and simple way.\u00a0\u00a0 In fact, it was astonishing, yet at the same time I was not surprised at all of their abilities.<\/p>\n

\"koch_\"six_star_geo\"When I first saw the formation with the central flower, I noticed that the flowers geometry housed six-pointed stars.\u00a0 So with an illustration, I showed how this exists (Fig. 5).\u00a0 Soon after I saw this, I saw that it held another set of six-pointed stars in its perimeter.\u00a0 There were twelve here (Fig. 6), creating a total of eighteen stars in the perimeter (Fig. 4).\u00a0 There were six groups of two.<\/p>\n

I knew there was more to be seen.\u00a0 Only I had no way of knowing where to look or in what direction.\u00a0 Days passed and I kept looking but nothing was crossing my path.\u00a0 I could feel there was something there.<\/p>\n

Then one evening, I went into a ceremony. During that ceremony, I received in a vision the answer I was looking for.\u00a0 I realized the answer I was looking for was like the crossing willows of my lodge.\u00a0 In my vision, I saw them bending in the wind, moving and crossing.\u00a0 I saw the stars beyond them.<\/p>\n

When the ceremony was completed, I went to my drawing.\u00a0 As I was looking at it, I saw the willows of my lodge in the drawing. They were connecting the stars together as one.
\n\"fractal_5_6\"<\/p>\n

I illustrated this in the way it had come to me in this vision (Fig. 7).\u00a0 The answer I was seeking was there.\u00a0 You see in my lodge the crossing willows create a star at the top of it.\u00a0 It was the same with the Starglyph.\u00a0 The crossing lines between the stars created a central star.\u00a0 It would be considered the thirteenth star.<\/p>\n

\"12_stars_13\"Those who understand numbers, know that twelve is considered one of the higher elements of spirit.\u00a0 Thirteen is a very sacred number in my ways, and was demonized over time by powers to be.\u00a0 It revealed the extreme abilities and universal levels that people where able to move within.<\/p>\n

This six-pointed star I found in the center of the drawing, is yet another level of an inner Koch Fractal as it is evolving (Fig. 8-9).\u00a0 It illustrates a never-ending flow to which we are connected.<\/p>\n

These series of stars show how this central flower of the Starglyph goes deeper and deeper in an infinite way, through the very center of the inner universe.\u00a0 So while the outer fractal continues to evolve in an infinite way outwardly (Fig.3), the inner will continue to evolve inwardly to the infinite.\u00a0 The following illustrations show the evolving sequence of the unfolding nature of the Starglyph.<\/p>\n

The Koch Fractal was one of the first Starglyphs I found which contained extensive amounts of hidden qualities.\u00a0 I spent a six month journey unfolding it’s content.\u00a0 Not only did it possess a tremendous amount of mathematical correlations, it had an equal amount of spiritual understandings related to my Native American ways. I found the Starglyph was like a running waterfall of geometric relationships of an infinite nature. As I was looking even deeper, I also had a vision there was a square involved with this Starglyph.\u00a0 Something kept pulling on me that this square, unusual as it might be, could reveal a universal truth. I placed a line between upper and lower arms of the Koch Fractal.\u00a0 I used the distance between them to create a perfect square. The Great Mystery (the Universe, Spirit), suggested I place a circle on its corners.\u00a0 When I did, I found an amazing correlation.\u00a0 When I placed the circle in this manner, the circle encompassed the perimeter of the entire Starglyph and its smaller circles (Fig.12).\u00a0 There was no mistake that it was intended.<\/p>\n

\"fractal_8_9\"\"fractal_10_11\"<\/p>\n

\"symbol_in_field\"In 1905 Helmig Von Koch, a mathematician, conceptualized the mathematics of the “fractal,” seen as the outer outline in these drawings. On Aug. 8, 1997 the Star Nation People gifted to the people of Earth the symbol in the center. My research has led me to believe that this symbol was never seen by mathematicians prior to it appearing in the fields of England. This symbol is the seed, the flower of life, and is the egg from where Koch’s Fractal would emerge.\u00a0 I would wish to gift at this point the name of this Fractal and would now call it after those to whom it belongs: “The Star Nation Fractal.”<\/p>\n

The placement of the circle was pure spirit. I could also see that it reflected a very important and ancient symbol from my traditions. This square and circle is found on some obscure pictographs on reservations here in North America, and is connected to my ancestors, the mound builders (Fig. 13). Some of these date back thousands of years. These ancient relatives knew of the importance of this concept of the circle and the square. One of our elders explained this to be an expression of our divine balance between our physical and spiritual roads. It is a mystical understanding people are beginning to learn to reawaken.<\/p>\n

\"circle_square1\"\"geo_highbank\"<\/p>\n

Right: One of the many Ancient Mound sites in Ohio, composed of a circle and a square. The larger circle is 20 acres; the square is 18 acres.<\/p>\n

It did not stop there. I kept feeling there was more to this vision and looked further into the square and circle.\u00a0 I felt called to resize and reposition the circle in a way that seemed to reflect an understanding important to the ancient Egyptian ways of spirit, and also my ancestral ways.\u00a0 It is a mathematical formula known as a squared-circle.\u00a0 In this mathematical expression, the square is the same size geometrically speaking as the circle.\u00a0 I did not know how to find or solve this mathematical formula to see if what I had uncovered was correct, so I contacted a mathematician and friend of mine, Michael Glickman.\u00a0 He worked within the crop circle community, so I asked him to see if what I had uncovered was correct. Within a short time, he returned my call astonished at the finding, saying to me, “Oh my god, do you know what is here?”\u00a0 I laughed, as I knew exactly what was there.\u00a0 A circle just touching the points of the star in relationship with this square, created a perfect squared-circle (Also Fig. 12).\u00a0 It is a symbol reflecting the elements of perfect balance as well as a symbol of chaos.\u00a0 It showed the harmonic qualities that exist between the earth and spirit, or the sky, that in truth, exist within all beings.<\/p>\n

The six-pointed star is carried by many nations on the planet as a geometric expression of a higher truth of the universe.\u00a0 The aboriginal of Australia, ancient Egyptian, the eastern peoples, Hindu and Buddhist, the Jewish people, all carry this understanding.\u00a0 Here, native people of North America carry this symbol as well.\u00a0 There is for example, Wanblee Zee Zee (Golden Eagle), a relative of mine that keeps a six-pointed star altar, as I keep one myself.\u00a0 He has written a book called the Maka Wicahpi Wicohan.\u00a0 These are Native American Sioux words meaning the universal and spiritual laws of the Creator reflecting the understanding of the six-pointed star.\u00a0 I assure you, this symbol is the coming together of the earth and the sky; a symbol of perfect balance.<\/p>\n

This article is little more than the title of the meaning of this star.\u00a0 It could take a very long time to understand its full meaning.\u00a0 We understand the six-pointed star when we are able to fully embody its concepts.\u00a0 Until then, it is only some thoughts passing through our logical minds.\u00a0 It is my belief the concepts of the six-pointed star are important for every person on the planet.\u00a0 It is why I believe the Star Nation People sent it to begin with.\u00a0 Because of the way the Star Nation People have sent this formation in the field, I would call it the Star Nations Six-pointed Star Altar.\u00a0 The nature of its hidden qualities, for me, reflect the essence of the understanding of the six-pointed star, as I know it to be so beautifully.<\/p>\n

\"mandelbrot_original\"There are a series of six unseen, six-pointed stars, of which one of them is illustrated in red (Fig. 15).\u00a0 The upper point of the red six stars is not visible in the field.\u00a0 There are six stars that would fit around the Koch Fractal if one looks closely.\u00a0\u00a0 There is an additional unseen six-pointed star created by the points of these stars in the center.\u00a0 I have colored it in a lighter yellow.\u00a0 When the ring of six-pointed arrows (blue) have been sized so that the center of each arrow finds each point of this unseen central star, then you have the exact geometry that was in the field, in this Starglyph under Milk Hill.<\/p>\n

This Starglyph is a flawless, relationship illustration, done in a way that I have never seen before.\u00a0 I can say that nothing has surfaced in the ten years to follow it.\u00a0\u00a0 We have an understanding of this Koch Fractal.\u00a0 So it is my belief the Star Nation People have taken a known understanding and have gifted an illustration that shows the components of the inner infinity and the Koch Fractal outer infinity, in a way never known before.<\/p>\n

Please note that the small circles within the central flower in the field, house the six-pointed star (illustrated in orange).\u00a0 They center in each six-pointed arrow (blue).\u00a0There are six, six-pointed arrows in a circle.\u00a0 Also if you look closely at the circle of arrows, the Koch fractal outer infinity is illustrated in purple.<\/p>\n

I would ask to what school of thought does the creator of this Starglyph belong?\u00a0 I would ask them how were you able conceptualize such a symbol of harmonic balance<\/span> with this geometric statement?\u00a0 Did you study at such universities as Cambridge,\u00a0 MIT,\u00a0 or Harvard?\u00a0 To what school of geometry has inspired you so deeply?\u00a0 I would perhaps ask why would you present such a geometric harmonic finding in a field of wheat, rather than perhaps in an article in a mathematics magazine or in a book with such other works of inspiration?\u00a0 Perhaps it wasn’t geometry at all but was a school of truth or faith.\u00a0 Then I would ask to what nation do you belong?\u00a0 This is not the traditional ways of the Native American, Buddhist, Christian or many others I am aware of.\u00a0 Is there a great elder of this nation that would be considered the father of your path?\u00a0 They talk of spiritual knowing not truly understood before in this way.\u00a0 I would like to sit before your elders of this way and listen to their knowing, for they have a deep understanding of the ways of human beings and the balance of the universe, in such a way never presented before.<\/p>\n

In my view point, those who made this Starglyph are of such spiritual evolvement, and possess such knowing, understanding, and connection, as to possibly have the ability of walking on water.<\/p>\n

With my truest and deepest appreciation,
\nWah-we-nah<\/p>\n

Bearcloud<\/p>\n","protected":false},"excerpt":{"rendered":"

In July, 1998 the Star Nations sent another Starglyph that was important for all people. It appeared under the white horse of Milk Hill, in Wiltshire, England.\u00a0Mathematically it is referred to as a >Koch Fractal.\u00a0 This glyph had an unusual geometric flower in its center. One of the elements I uncovered as I was working […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":145,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-372","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/pages\/372","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/comments?post=372"}],"version-history":[{"count":0,"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/pages\/372\/revisions"}],"up":[{"embeddable":true,"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/pages\/145"}],"wp:attachment":[{"href":"http:\/\/www.bearcloudgallery.com\/starnationgallery\/wp-json\/wp\/v2\/media?parent=372"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}