{"id":1061,"date":"2010-04-12T01:42:28","date_gmt":"2010-04-12T05:42:28","guid":{"rendered":"http:\/\/orbittrap.ca\/?p=1061"},"modified":"2010-04-12T01:53:28","modified_gmt":"2010-04-12T05:53:28","slug":"hydra-sculptures-from-the-4th-dimension","status":"publish","type":"post","link":"https:\/\/orbittrap.ca\/?p=1061","title":{"rendered":"Hydra: Sculptures from the 4th Dimension"},"content":{"rendered":"

Another program from the extensive digital treasury<\/a> of Terry Gintz.\u00a0 Unlike Fractal Vizion which contains, metaphorically speaking, a full fractal orchestra, Hydra<\/a> is a solo performance where the star is the quaternion, a richly talented Pavarotti of the fractal world who needs not even a piano for accompaniment.<\/p>\n

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I mixed Time with Space...<\/p><\/div>\n

Perhaps the label Michelangelo of the Fractal World<\/em> would be better since quaternions are 3 dimensional –or more correctly, 4 dimensional– and therefore resemble sculptures more than paintings.\u00a0 There’s been a lot of excitement lately about the (so-called) 3D mandelbrot, the Mandelbulb, but here’s something I find more visually exciting as much as it’s practically ancient as far as fractals and fractal art goes.<\/p>\n

Quaternionic algebra was introduced by Irish mathematician Sir William Rowan Hamilton in 1843. However the use of quaternions to describe rigid body orientations has a much older history dating back to at least 1776 in the work of Euler.
\nHamilton knew that the complex numbers could be viewed as points in a plane, and he was looking for a way to do the same for points in space. Points in space can be represented by their coordinates, which are triples of numbers, and for many years Hamilton had known how to add and multiply triples of numbers. But he had been stuck on the problem of division: He did not know how to take the quotient of two points in space.
\nThe breakthrough finally came on Monday 16 October 1843 in Dublin, when Hamilton was on his way to the Royal Irish Academy where he was going to preside at a council meeting. While walking along the towpath of the Royal Canal with his wife, the concept behind quaternions was taking shape in his mind. Hamilton could not resist the impulse to carve the formulae for the quaternions i2 = j2 = k2 = ijk = -1<\/strong> into the stone of Brougham Bridge as he passed by it.<\/p>\n

http:\/\/en.wikipedia.org\/wiki\/Quaternion#History<\/a><\/p><\/blockquote>\n

Most fractal things (are quaternions fractals?) take their origin from the work of Benoit Mandelbrot in the latter part of the 20th century, but here’s something dating back to 1843 and in part to 1776.\u00a0 Euler?\u00a0 Yikes.\u00a0 He was Ancient Greek or something, like Pythagoras and Copernicus.\u00a0 Close enough.\u00a0 Let’s get to the pictures.<\/p>\n

Thanks to Mr. Gintz’s programming expertise all we have to do is push some buttons and play with the color palettes.\u00a0 I’m not really sure what a quaternion is, but that just adds some magic to the recipe.\u00a0 Here’s a quote that shows I’m not the only person a little disoriented by the concept of a quaternion:<\/p>\n

Time is said to have only one dimension, and space to have three dimensions. [\u2026] The mathematical quaternion partakes of both these elements; in technical language it may be said to be “time plus space”, or “space plus time”: and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be.” \u2014 William Rowan Hamilton (Quoted in R.P. Graves, “Life of Sir William Rowan Hamilton”).<\/p><\/blockquote>\n

Actually, that helps a bit: “a reference to four dimensions”.\u00a0 It’s got four numbers instead of three.\u00a0 Like a tricycle with a steering wheel.\u00a0 Hypernion<\/em>, on the other hand, doesn’t even bring up a page on the Wikipedia and a Google search for it just suggests that I’ve made a spelling mistake.\u00a0 Anyhow, on to the pictures.\u00a0 Or videos, rather…
\n[flashvideo file=http:\/\/ambaka.com\/blog\/26\/hydra22.flv width=360 height=296\u00a0 \/]<\/p>\n

I like this one.\u00a0 I like it a lot.\u00a0 And I don’t care if it does<\/em> look like the stopper from a\u00a0 champagne bottle.
\n[flashvideo file=http:\/\/ambaka.com\/blog\/26\/hydra06.flv width=340 height=360\u00a0 \/]<\/p>\n

.<\/p>\n

I did a video capture to show you the interesting way in which they’re made.\u00a0 The color gradient silhouette is just a draft of the final image, but sometimes that temporary image has interesting qualities of it’s own.\u00a0 There’s not a whole lot of animation really, just a slow revealing of the silhouette, so for simplicity and better image quality I saved a few silhouettes to compare with the final images.\u00a0 Just like with Fractal Vizion’s L-system and Fractal Landscape creation, Hydra’s quaternion images have an extra dimension to them, that being the cool way in which they’re produced.<\/p>\n

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Temporary Silhouette<\/p><\/div>\n

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Final Image<\/p><\/div>\n

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Sihouette<\/p><\/div>\n

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Final Image<\/p><\/div>\n

Here’s a few more to give you an idea of what the program can do.\u00a0 I should mention that Hydra comes with a nice Help file but that I didn’t look at it until after I’d made all these images.\u00a0 The program is pretty straightforward and hides the complexity of quaternion creation behind a couple of menus with easy to chose options.\u00a0 Another nice touch is the addition of a random generation button which seems to be a trademark of Terry Gintz’s programs.\u00a0 He really makes it easy for you to get started right away and then to start experimenting.\u00a0 That’s the kind of algorithmic art programming that I like.\u00a0 These next two are Hypernions.<\/p>\n

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I like the ancient artifact look<\/p><\/div>\n

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The hypernions have squarish characteristics<\/p><\/div>\n

The coloring is great to work with.\u00a0 Open the palette editor and just click on the random palette button.\u00a0 After that there’s a few simple adjustments you can make to alter the palette.\u00a0 The images you see here are custom palettes I made this way.\u00a0 The whole thing is pretty intuitive.\u00a0 Not all fractal programs are this easy to use.\u00a0 Here’s my two palettes if you’re interested in trying them out in the program: bluewrap.pqz<\/a> and yellow-clay.pqz<\/a><\/p>\n

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I think it's map of North America<\/p><\/div>\n

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Ice cream, but true-colored ice cream<\/p><\/div>\n

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More ice cream<\/p><\/div>\n

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Sometimes Hydra makes some really surprising things<\/p><\/div>\n

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Sometimes they're just interesting stones to collect<\/p><\/div>\n

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This one looks rather fractal and very lifelike. Reminds me of the wind carved stone formations in the Southwest U.S.<\/p><\/div>\n

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This is one is a zoomed-in detail from the surface of a quaternion<\/p><\/div>\n

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Some experimenting. Hydra does very nice texturing. They really are like sculptures.<\/p><\/div>\n

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Different palette. Hypernion formula. Whatever that is.<\/p><\/div>\n

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Just a nice rock to add to the collection<\/p><\/div>\n

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Hypernion. A square version of the image from the start of this blog posting.<\/p><\/div>\n

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I find these clay constructions quite intriguing and I want to try out every formula and its variations. That's how I found this one.<\/p><\/div>\n

Well, what else is there to say or show?\u00a0 You can rotate the quaternions just like any other kind of sculpture and view them from different angles, lighting, surface texture and other variable characteristics.\u00a0 It makes Ice Cream and Islands; Bubble Gum of the Gods; Brush Stroke Drafts and something new that I’ve termed computoids<\/em> after the word asteriods in the sense of exotic computer made rocks.\u00a0 Perhaps you have to be a bit of a rock collector to really enjoy this program.\u00a0 It’s got a real natural style to what it does.\u00a0 And style is what I think is very important in fractal art and algorithmic art programs in general.\u00a0 Hydra produces imagery that is visually appealing.\u00a0 There’s other programs that can render the complex formulas you find in Hydra, but they don’t render them in the same graphically appealing ways as Hydra does.\u00a0 Great programs like this take more than just technical talent to make they take artistic talent as well.\u00a0 There’s a lot of artistry that programmers like Terry Gintz put into programs like Hydra.\u00a0 That’s why it’s so easy for people like me who just push buttons to make interesting stuff with them.\u00a0 There’s an awful lot of power in those buttons.<\/p>\n","protected":false},"excerpt":{"rendered":"

Another program from the extensive digital treasury of Terry Gintz.\u00a0 Unlike Fractal Vizion which contains, metaphorically speaking, a full fractal orchestra, Hydra is a solo performance where the star is the quaternion, a richly talented Pavarotti of the fractal world who needs not even a piano for accompaniment. Perhaps the label Michelangelo of the Fractal … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":1062,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-1061","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2010\/04\/hydra34-big.png?fit=600%2C450&ssl=1","jetpack-related-posts":[{"id":409,"url":"https:\/\/orbittrap.ca\/?p=409","url_meta":{"origin":1061,"position":0},"title":"Fractal Art Without a Computer?","author":"Tim","date":"11 September, 2009","format":false,"excerpt":"Could this work be described as ...Fractal?Admiral Otto Von Howitzerhead by Kris Kuksi 2009Samuel Monnier, writing at Algorithmic Worlds, his new website - gallery - and blog, said some very interesting things about the fractal nature of sculptures done by Kris Kuksi.\u00a0 Sam said that Kris Kuksi's scuptures \"are very\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":411,"url":"https:\/\/orbittrap.ca\/?p=411","url_meta":{"origin":1061,"position":1},"title":"Phase Two: A Real Fractal Art Exhibition","author":"cruelanimal","date":"17 September, 2009","format":false,"excerpt":"Swine Flu by Luke Jerram I think Tim's recent observations that fractal art is about to undergo into a new Phase Two paradigm shift are on target. Fractal art will never evolve beyond a curious, trippy, decorative craft until it moves away from being defined by software and instead starts\u2026","rel":"","context":"With 2 comments","block_context":{"text":"With 2 comments","link":"https:\/\/orbittrap.ca\/?p=411#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2009\/09\/JackieJokers_recursion.jpg?fit=337%2C500&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":3009,"url":"https:\/\/orbittrap.ca\/?p=3009","url_meta":{"origin":1061,"position":2},"title":"Fractals: A New Medium","author":"Tim","date":"22 September, 2011","format":false,"excerpt":"I think I've found a better way to explain what makes fractal art so different than other art forms.\u00a0 The differences are there simply because fractals themselves are a different medium to work with.\u00a0 Fractals are different than paint and canvas or chisel and stone. In fact, fractals are probably\u2026","rel":"","context":"With 1 comment","block_context":{"text":"With 1 comment","link":"https:\/\/orbittrap.ca\/?p=3009#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2011\/09\/Zon9.jpg?fit=500%2C500&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":362,"url":"https:\/\/orbittrap.ca\/?p=362","url_meta":{"origin":1061,"position":3},"title":"Fractal Woodburning","author":"Tim","date":"28 January, 2009","format":false,"excerpt":"I'm not making this up.\u00a0 I went surfing about to see what I could find in the fractal world and lo and behold at Flickr, a couple of pages into a search on the term \"fractal\", I saw wires, boards and strange, curly burn patterns.photo by AetherPhoto caption from Aether's\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":346,"url":"https:\/\/orbittrap.ca\/?p=346","url_meta":{"origin":1061,"position":4},"title":""I Don’t Have to Show You Any Stinkin’ Software"","author":"cruelanimal","date":"22 September, 2008","format":false,"excerpt":"If you're the fractal police, where is your software? Aaah, leave it to the cutting edge crowd over at Keith MacKay's idreamincolor forum to ask the big questions and come up with the big-headed answers. Over a month ago, MacKay posited this head-scratcher:Lately I have been wondering if we have\u2026","rel":"","context":"With 2 comments","block_context":{"text":"With 2 comments","link":"https:\/\/orbittrap.ca\/?p=346#comments"},"img":{"alt_text":"Stinkin' software...","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2008\/09\/stinkinsoftware.jpg?fit=500%2C376&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":166,"url":"https:\/\/orbittrap.ca\/?p=166","url_meta":{"origin":1061,"position":5},"title":"Mysteries of Faith and Art","author":"cruelanimal","date":"5 March, 2007","format":false,"excerpt":"Why did the fractal cross the road?To travel back in time?Compare this image: The familiar Mandelbrot Set form. With this image:An Ottoman illustration of the sacrifice of Ismael (1583). The resemblance should not be a surprise. 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