{"id":4358,"date":"2012-12-12T11:30:53","date_gmt":"2012-12-12T16:30:53","guid":{"rendered":"http:\/\/orbittrap.ca\/?p=4358"},"modified":"2012-12-12T11:30:53","modified_gmt":"2012-12-12T16:30:53","slug":"pauldelbrots-mandelbrot-safari-and-other-journeys-into-the-unknown","status":"publish","type":"post","link":"https:\/\/orbittrap.ca\/?p=4358","title":{"rendered":"Pauldelbrot’s Mandelbrot Safari and other Journeys into the Unknown"},"content":{"rendered":"

Back, several postings ago, when I reviewed<\/a> the latest Fractalforums.com calendar, I heaped abuse on Pauldelbrot’s image from his Mandelbrot Safari<\/em> series calling it retro and not cutting-edge.\u00a0 The owner of Fractalforums.com and publisher of the calendar, Christian Kleinhuis, informed me that what Pauldelbrot was doing was in fact very cutting-edge as it was utilizing new methods that enabled him to zoom to a much greater extent than had previously been possible.\u00a0 And something about a new coloring method too.<\/p>\n

\"\"

From Atomic Pulp<\/a><\/p><\/div>\n

But as an illustration of how weird fractal art as an art form can be, Pauldelbrot’s work can be kicked and abused in one review and then praised in another, just a month later as you will soon see.<\/p>\n

Let me explain this apparently senseless thinking:\u00a0 For the calendar, I didn’t think Pauldelbrot’s work had commercial appeal (as well as just about everyone else’s work in the calendar); But in this posting I present his Mandelbrot Safari<\/em> images as epitomizing the pastime of fractal exploration (and a fresh example of that) as well as a good example of classic-style fractal art.<\/p>\n

But most importantly, I rather like many of these images myself for their own sake, and the fact that they’re from the Outer Limits<\/em> just enhances that.\u00a0 One shouldn’t talk too much about fractal art.\u00a0 Perhaps most readers have already skipped to the pictures.<\/p>\n

The best way to follow the Mandelbrot Safari<\/em> is by reading its own forum thread<\/a> on Fractalforums.com.\u00a0 More images, comments, etc…\u00a0 Who knows?\u00a0 You might even decide to buy one of the FFs 2012 calendars<\/a> for no other reason than because it contains one of these Safari<\/em> images.\u00a0 Now wouldn’t that make me look stupid after saying they had no commercial appeal?\u00a0 Buy a calendar —fight the man!<\/em><\/p>\n

~Click on images to go to original forum thread with larger images in it~<\/em><\/p>\n

\"\"<\/a>

The initial image from Pauldelbrot’s Mandelbrot Safari thread<\/p><\/div>\n

The safari begins:\u00a0 fairly common terrain we’re starting off from on May 4th, 2012.\u00a0 Doesn’t look particularly promising, I must say.\u00a0 But I’m not the pilot or the navigator on this expedition.\u00a0 Let’s wait and see what’s over the horizon.\u00a0 I’m sure he’s got some exotic destination in mind.<\/p>\n

\"\"<\/a>

evdz1_008_lrg by Pauldelbrot<\/p><\/div>\n

The game is afoot, as Sherlock Holmes would say.\u00a0 That’s an odd looking color to be seeing out in this sargasso sea of yellow.\u00a0 The perennial question:\u00a0 Where does it go?<\/em><\/p>\n

\"\"<\/a>

evdz1_017 by Pauldelbrot<\/p><\/div>\n

I jumped ahead a few of Pauldelbrot’s image postings and here we are at the first of many “portals” to the (glittering) unknown.\u00a0 If you’re anything of a fractalnaut, you ought to be getting excited right now because it looks like this trip is 1. never going to end, and 2. going to be full of surprises.<\/p>\n

\"\"<\/a>

evdz1_018_lrg by Pauldelbrot<\/p><\/div>\n

A comment:<\/p>\n

\"\"

Is that the coloring of Pauldelbrot’s image, or of this guy’s hefty signature?\u00a0 (sorry, couldn’t resist; it’s the duty of everyone on the internet to stamp out signature lines and other forms of “junk mail” content)<\/p><\/div>\n

\"\"<\/a>

evdz1_029_lrg by Pauldelbrot<\/p><\/div>\n

According to the thread<\/a>, we’re now zoomed into about 4 e30 magnification.\u00a0 That’s 4 and thirty zeroes behind it.<\/p>\n

\"\"<\/a>

evdz1_044 by Pauldelbrot<\/p><\/div>\n

Pauldelbrot answers a tech question in the thread here about what program he’s using:<\/p>\n

…a mix of custom and off-the-shelf code here. Time on these has increased but the latest few have taken a few hours each. The iterations are still pretty low (around 5000) but the precision bits are getting fairly numerous.<\/p><\/blockquote>\n

A couple hours, each?\u00a0 We’re obviously on the other side of some computing sound barrier.<\/p>\n

\"\"<\/a>

evdz1_090 by Pauldelbrot<\/p><\/div>\n

Note by author:<\/p>\n

Now over 20,000 iterations in the shallowest parts of each image, and the magnification has just passed one googol, too…<\/p><\/blockquote>\n

Sound sci-fi -ish, doesn’t it?\u00a0 What’s a googol?\u00a0 Biggy big!\u00a0 So big it’s covered with big-fur!\u00a0 That’s the layman’s definition. (it’s this, actually: 10100<\/sup>)<\/p>\n

Gets slower and slower with depth…<\/p><\/blockquote>\n

He’s doing this in Ultrafractal (UF) and makes this comment which sheds some light on the type of technical challenge all this is:<\/p>\n

I should warn you that to get close to the quality results I’ve posted you’d need to use 3×3 AA, depth 2, nonadaptive AA because depth 1 isn’t enough oversampling and UF’s adaptive AA seems not to work as well as mine. The deeper images would thus need some very<\/em> beefy hardware to render in anywhere near<\/em> a reasonable time; or even a cluster rendering different tiles of the image per machine.<\/p><\/blockquote>\n

This is what Christian Kleinhuis, the owner (and sponsor) of Fractalforums.com must have meant when he told me Pauldelbrot’s image in the calendar was actually cutting edge imagery after all.<\/p>\n

\"\"<\/a>

evdz1_113 by Pauldelbrot<\/p><\/div>\n

The images are largely like this; circular and elegant, which is the sort of thing that characterizes classic fractal art –highly detailed, organized images.\u00a0 I guess “complex geometric” is not a bad description, either.<\/p>\n

Pauldelbrot says this in response to a comment about the great coloring:<\/p>\n

It “discovers” colors, because it keeps shifting and blending them. Colors that are somewhat between pure primaries and secondaries, or somewhat desaturated as well as saturated, included, which may often be overlooked by humans doing things manually.<\/p><\/blockquote>\n

\"\"<\/a>

evdz1_204 by Pauldelbrot<\/p><\/div>\n

“Overlooked by humans doing things manually”\u00a0 Computers are more than just powerful paintbrushes.\u00a0 It’s through this sort of exploration that one can develop a real appreciation for the machinery that they’re using.\u00a0 That’s half the fun, I’d say.<\/p>\n

I’ve just shown a sampling of images here; you’ll definitely want to check out the thread<\/a> if you find these interesting.<\/p>\n

\"\"<\/a>

evdz1_218 by Pauldelbrot<\/p><\/div>\n

Some of the really dark images are the best in my opinion.\u00a0 This one is from November 30th, 2012 and marks the 7th month of the safari.\u00a0 It’s still going on, although, as Pauldelbrot said, the rendering gets slower because of the depth of the zoom.\u00a0 Another image was posted just this week (Dec 11).<\/p>\n

Pauldelbrot has embarked on a number of these zoom excursions with the same journey into the unknown feel to them.\u00a0 Here’s some highlights from some of the others…<\/p>\n

\"\"<\/a>

511_28_11_12_2_35_18 by Pauldelbrot<\/p><\/div>\n

A note from this image, from a series entitled “Fall Woods 1”:<\/p>\n

This zoom is near the Autumn Forest zoom. However, the area zoomed into is around a seahorse below and to the right of the green period-3 blob in Autumn Forest I. Out here, the “zero basin” doesn’t exist — there is no zero attractor at all. Where that happens, the basin implodes into a disconnected Julia set, which the surrounding seahorse shapes still try to conform to, with amazingly convoluted results!<\/p>\n

Images in this series have mostly been rendered at 32000×24000 and downsampled for a whopping 625 samples per pixel, needed<\/strong> to render the “zero basin Julia” regions properly. I was able, nonetheless, to render most of them in under two hours.<\/p><\/blockquote>\n

Yeah, that’s 32 –thousand<\/em> by 24-thousand<\/em>.\u00a0 Pauldelbrot is no wimp when it comes to making fractals!<\/p>\n

\"\"<\/a>

511_03_11_12_12_37_51 by Pauldelbrot<\/p><\/div>\n

\"\"<\/a>

511_02_11_12_12_20_32 by Pauldelbrot<\/p><\/div>\n

Those above are two of my personal favorites from the Autumn Forest II and I series.\u00a0 The disorienting vastness of fractal panoramas is easily seen in both as well as Pauldelbrot’s excellent coloring style.\u00a0 In the process of trying to make fractals into<\/em> art, I wonder how many of us forget how artistic fractals can be in their raw, freshly calculated form –if only we were to explore them<\/em> and not the latest layering techniques more.<\/p>\n

\"\"<\/a>

Lilac Exponent by Pauldelbrot, Sept 14, 2011<\/p><\/div>\n

This is from more than a year ago.\u00a0 It caught my eye back then because of the intense patterns of shapes and shapes and more shapes<\/em>.\u00a0 This sort of thing is an art form that only fractal algorithms can do and they do it very well, especially at the hands of someone as talented and creative as Pauldelbrot.<\/p>\n

As Christian Kleinhuis was saying; Pauldelbrot has really done something new and different even if it does lie within the old category of “classic” fractal art.\u00a0 I think Pauldelbrot has elevated that classical category higher with this kind of work and his probably represents the best of its kind.<\/p>\n

Best of its kind so far, that is.\u00a0 If Pauldelbrot’s herculean efforts and endless hours of rendering have shown one thing, it’s that there’s still much to be explored even in the realm of classical fractal imagery.\u00a0 I hope he’s inspired a few others to follow this path, even if it takes them away from the seemingly much more advanced 3D fractals that most work on these days.<\/p>\n","protected":false},"excerpt":{"rendered":"

Back, several postings ago, when I reviewed the latest Fractalforums.com calendar, I heaped abuse on Pauldelbrot’s image from his Mandelbrot Safari series calling it retro and not cutting-edge.\u00a0 The owner of Fractalforums.com and publisher of the calendar, Christian Kleinhuis, informed me that what Pauldelbrot was doing was in fact very cutting-edge as it was utilizing … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":4360,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_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":""},"categories":[1],"tags":[],"class_list":["post-4358","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\/2012\/12\/1.png?fit=457%2C447&ssl=1","jetpack-related-posts":[{"id":4027,"url":"https:\/\/orbittrap.ca\/?p=4027","url_meta":{"origin":4358,"position":0},"title":"Brother, can you spare $58?","author":"Tim","date":"31 October, 2012","format":false,"excerpt":"Fractalforums.com's owner, Christian Kleinhuis (aka Trifox) is attempting to put out another fractal art calendar this year.\u00a0 I reviewed last year's and called it, \"The Best Fractal Calendar Ever!\". I hope that review scored me enough points over there with the Fractalforums.com folks to cover this year's review. Here's a\u2026","rel":"","context":"With 2 comments","block_context":{"text":"With 2 comments","link":"https:\/\/orbittrap.ca\/?p=4027#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2012\/10\/58.jpg?fit=402%2C326&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":3572,"url":"https:\/\/orbittrap.ca\/?p=3572","url_meta":{"origin":4358,"position":1},"title":"Best Fractal Calendar Ever!","author":"Tim","date":"1 December, 2011","format":false,"excerpt":"Christian Kleinhuis of Fractalforums.com has just published a 2010 fractal calendar. Featuring the best artwork form Fractalforums.com and printed large size and spiral bound, it hopefully marks a new era in fractal art publishing. A review of the images and background on how the project came about.","rel":"","context":"With 1 comment","block_context":{"text":"With 1 comment","link":"https:\/\/orbittrap.ca\/?p=3572#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2011\/12\/51elm7iQIJL._SL500_.jpg?fit=500%2C353&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":401,"url":"https:\/\/orbittrap.ca\/?p=401","url_meta":{"origin":4358,"position":2},"title":"Is It Official?","author":"Tim","date":"18 August, 2009","format":false,"excerpt":"The rules page on the official website for the Benoit Mandelbrot Fractal Art Contest 2009 was changed overnight.\u00a0 The list of the Selection Panel Members (judges) has been abbreviated and now no longer includes the name of\u00a0 Garth Thornton who yesterday announced his intention to resign on Fractalforums.com.New Page (above)Old\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1179,"url":"https:\/\/orbittrap.ca\/?p=1179","url_meta":{"origin":4358,"position":3},"title":"2010 Nobel Prize for Fractal Art","author":"Tim","date":"12 May, 2010","format":false,"excerpt":"For his work in discovering the Mandelbox formula of 3-D fractals, the winner is Tom Lowe, better known on Fractalforums.com as Tglad. Now some might ask why Daniel White and the Mandelbulb Team weren't this year's Nobel recipients, but while the Mandelbulb discovery was truly the most exciting event in\u2026","rel":"","context":"With 2 comments","block_context":{"text":"With 2 comments","link":"https:\/\/orbittrap.ca\/?p=1179#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2010\/05\/mandelbox3.png?fit=500%2C451&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1135,"url":"https:\/\/orbittrap.ca\/?p=1135","url_meta":{"origin":4358,"position":4},"title":"FractalForums.com Spring 2010 Competition","author":"Tim","date":"2 May, 2010","format":false,"excerpt":"I found this email in my inbox just yesterday and quickly felt my fractal art commentary sap rising boldly in my branches.\u00a0 Here, read it carefully and see if it has the same Spring-Time for Fractaland effect on you: FractalForums.com Spring 2010 Fractal Art Competition Submission Period has Ended The\u2026","rel":"","context":"With 7 comments","block_context":{"text":"With 7 comments","link":"https:\/\/orbittrap.ca\/?p=1135#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2010\/05\/living-ornaments.jpg?fit=500%2C500&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":357,"url":"https:\/\/orbittrap.ca\/?p=357","url_meta":{"origin":4358,"position":5},"title":"Another Scammy Contest, Or Just A Little Fun?","author":"Tim","date":"17 December, 2008","format":false,"excerpt":"Chrimbo-Tree by twinbee posted to Fractalforums.com\"Cash prize has swelled from $10 to $20 now\"\"Yes, there's prizes. However, to be eligible, I need at least 2 entries.\"\"Prizes include......Brand new optical illusions I created myself (I usually charge for these from my site)......Lifetime subscription to MegaDJ. This will only be useful if\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/4358","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4358"}],"version-history":[{"count":14,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/4358\/revisions"}],"predecessor-version":[{"id":4389,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/4358\/revisions\/4389"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/media\/4360"}],"wp:attachment":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}