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September 25, 2011
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Fractal Wallpaper by coyotemax Fractal Wallpaper by coyotemax
First foray into 3d fractals.
Created with Mandelbulb, whatever the latest version is. I tried using a tutorial but it was written for a previous version so kind of difficult to navigate ;)

Anyhow after some messing around I came up with this.

Is it art? or is is it just math? is it a combination of the two?

No idea, but it looks good on my desktop as wallpaper ;P
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:iconreverend23:
reverend23 Featured By Owner May 19, 2012
It's math-y art!
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:iconcoyotemax:
coyotemax Featured By Owner May 20, 2012  Hobbyist Digital Artist
or artsy math!
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:iconrjl7983:
RJL7983 Featured By Owner Feb 18, 2012
Numbers are an amazing thing especially the things you can do with numbers, you can take two or more concepts in mathematics and joine them like taking positive and negative operations and puttings them on a coordiante system. Before I go into this I need to explain what some notations mean to get an idea of how big the numbers get or how they are represented. Exponentiation is obviously repeated Multiplication but the fourth operation Tetration is the next operation up and is repeated Exponentiation for example 7 Tetrated to 10 would be 7^7^7^7^7^7^7, 149 Tetrated to 6 would be 149^149^149^149^149^149, 5 Tetration to 11 would be 5^5^5^5^5^5^5^5^5^5^5 and 7 Tetration to 3 would be 7^7^7 so imagine what other numbers would be, Pentation would be the next operation up from Tetration or repeated Tetration, there would be at least as much difference between Tetration and Pentation as there would be Exponentiation and Tetration, I had to say these first.

You could make a type of X axis of mathematical operations and their likewise names, this is really a series of operations you could make with assigning names and fitting syntax alittle that would be something like this. Negative Eightation (The negative Eightillionth notation, this would be 10^-3x10^3x10^240+3), Negative Fiftation (The negative Fiftillionth notation, this would be 10^-3x10^3x10^150+3), Negative Thirtation (The negative Thirtillionth notation, this would be 10^-3x10^3x10^90+3), Negative Octekation (The negative Octekillionth notation, this would be 10^-3x10^3x10^54+3), Negative Vekation (The negative Vekillionth notation, this would be 10^-3x10^3x10^30+3), Negative Hectillation (The negative Hectillionth notation, this would be 10^-3x10^300+3), Negative Icosation (The negative Icosillionth notation, this would be 10^-3x10^60+3), Negative Tetrecation (The negative Tetrecillionth notation, this would be 10^-3x10^42+3), Negative Picillation (The negative Picillionth notation, this would be 10^-3x10^12+3), Negative Nongentation (The negative Nongentillionth notation, this would be 10^-2703), Negative Ducentillation (The negative Ducentillionth notation, this would be 10^-603), Negative Centillation (The nagative Centillionth notation, this would be 10^-03), Negative Quinquagintation (The negative Quinquagintillionth notation, this would be 10^-153), Negative Trigintation (The negative Trigintillionth notation, this would be 10^-93), this is a engative seperation of metric rpefixes and names of true numbers, Rimtation (The 10^-45 notation), Sotration (The 10^-42 notation), Trektation (The 10^-39 notation), Untation (The 10^-36 notation), Planckation (The 10^-35 notation), Vunktation (The 10^-33 notation), Wektation (The 10^-30 notation), Xontation (The 10^-27 notation), Yoctation (The 10^-24 notation), Zeptation (The 10^-21 notation), Attation (The 10^-18 notation), Femptation (The 10^-15 notation), Pication (The -1,000,000,000,000 notation), Nanation (The -1,000,000,000 notation), Micration (The -1,000,000 notation), Millation (The -1,000 notation), Centation (The -100 notation), this is the negative seperation of latin prefix numbers and metric prefixes, Negative Decation (The -10 notation), Noventation (The -9 notation), Negative Octation (The -8 notation), Septation (The -7 notation), Sexation (The -6 notation), Quintation (The -5 notation), Quadation or Negative Tetration (The -4 notation), Negative Exponentiation (The -3 notation), Division (The -2 notation), Subtraction (The -1 notation), Zeration (The 0 notation), Addition (The 1 notation), Multiplication (The 2 notation), Exponentiation (The 3 notation), Tetration (The 4 notation), Pentation (The 5 notation), Hexation (The 6 notation), Heptation (The 7 notation), Octation (The 8 notation), Nonation (The 9 notation), Decation (The 10 notation), Undecation (The 11 notation), somewhere here maybe before the prefixes of these operations goes from being based off latin prefixes of numbers to metric prefixes indicating the number of the mathematical operation, Hectation (The 100 notation), Kilation (The 1,000 notation), Megation (The 1,000,000 notation), Gigation (The 1,000,000,000 notation), Teration (The 1,000,000,000,000 notation), Petation (The 10^15 notation), Exation (The 10^18 notation), Zettation (The 10^21 notation), Yattation (The 10^24 notation), Xonation (The 10^27 notation), Wekation (The 10^30 notation), Vundation (The 10^33 notation), Udation (The 10^36 notation), Tredation (The 10^39 notation), Sortation (The 10^42 notation), Rintation (The 10^45 notation), what happen between here is the operations being named are no longer based on latin or metric prefixes but are based on seemless veryations on the numbers they are derived from like Trigintation for example will have a name that is prefixed similar to the name of the number it's self and sence Tringintation would be the trigintillionth operation then it name would likewise be Trigintation thus starting the third class of operations not based on metric prefixes but on the number name they represent or level, Trigintation (The Trigintillionth notation, a Trigintillion is 10^93), Quinquagintation (The Quinquagintationth notation, a Quinquagintillion is 10^153), Centillation (The Centillionth notation, a Centillion is 10^303), Ducentillation (The Ducentillionth notation, a Ducentillion is 10^603), Nongentation (The Nongentillionth notation, A Nongentillion is 10^2703), Picillation (The Picillionth notation, a Picillion is 10^3x10^12+3), Tetrecation (The Terecillionth notation, a Tetrecillion is 10^3x10^42+3), Icosation (The Icosillionth notation, an Icosillion is 10^3x10^60+3), Hectillation (The Hectillionth notation, a Hectillion is 10^3x10^300+3), Vekation (The Vekillionth notation, a Vekillion is 10^3x10^3x10^30+3), Octekation (The Octekillionth notation, an Octekillion is 10^3x10^3x10^54+3), Thirtation (The Thirtillionth notation, a Thirtillion is 10^3x10^3x10^90+3), Fiftation (The Fiftillionth notation, a Fiftillion is 10^3x10^3x10^150+3), Eightation (The Eightillionth notation, an Eightillion is 10^3x10^3x10^240+3), Potation (The Potillionth notation, a Potillion is 10^(3x10^(3x10^1500) +3)), Notillation (The Notillionth notation, a Notillion is 10^(3x10^(3x10^2700) +3)), Zalation (The Zalillionth notation, a Zalillion is 10^(3x10^(3x10^21,000) +3)), Awkation (The Awkillionth notation, an Awkillion is 10^(3*10^ (3*10^300,000,000) +3)), Solation (The Solillionth notation, a Solillion is 10^(3x10^(3x10^3septillion) +3)), Gaxation (The Gaxillionth notation, a Gaxillion is 10^(3x10^(3x10^3decillion) +3)), Multation (The Multillionth notation, a Multillion is 10^(3x10^(3x10^3tredecillion) +3)), Googolquadriplexation (The Googolquadriplexth notation, a Googolquadriplex is 10^10^10^10^10^100), Googolseptaplexation (The Googolseptaplexth notation, a Googolseptaplex is 10^10^10^10^10^10^10^10^100), Googolnonaplexation (The Googolnonaplexth notation, a Googolnonaplex is 10^10^10^10^10^10^10^10^10^10^100), Tripentation (The Tripenth notation, a Tripent is 5 pentated to 5), Gaggolplexation (The Gaggolplexth notation, a Gaggolplex is 10 pentated to gaggol), Triseptation (The Triseptianth notation, a Trisept is 7 heptated to 7), Gagolplexation (The Gagolplexianth notation, a Gagolplex is {10,gagol,9}), Boogolplexation (The Boogolplexianth notation, a Boogolplex is {10,10,boogol}), Biggation (The Biggolth notation, a Biggol is {10,10,100,2}), Beegolplexation (The Beegolplexianth notation, a Beegolplex is {10,10,beegol,4}), Tetratration (The Tetratrith notation, a Tetratri is {3,3,3,3}), Triggation (The Triggolth notation, a Triggol is {10,10,10,100,2}), Treegation (The Treegolth notation, a Treegol is {10,10,10,100,4}), Pentadecation (The Pentadecalth notation, a Pentadecal is {10,10,10,10,10}), Quadriggolplexation (The Quadriggolplexianth notation, a Quadriggoplex is {10,10,10,10,quadriggol,2}), Quadroggation (The Quadroggolth notation, a Quadroggol is {10,10,10,10,100,6}), Pentatration (The Pentatrith notation, a Pentatri is {3,3,3,3,3}), Quinteegation (The Quinteegolth notation, a Quinteegol {10,10,10,10,10,100,4}), Octadecation (The Octadecalth notation, an Octadecal is {10,10,10,10,10,10,10,10}), Sextoogation (The Sextoogolth notation, a Sextoogol is {10,10,10,10,10,10,100}), Iteralplexation (The Iteralplexianth notation, an Iteralplex is {10,10,10,10,10,10,...........,10,10,10} (iteral 10's)), Truperdecation (The Truperdecalth notation, a Truperdecal is {10,duperdecal (1) 2}), Geebation (The Geebolth notation, a Geebol is {10,100,4 (1) 2}), Bibbation (The Bibbolth notation, a Bibbol is {10,10,100,2 (1) 2}), Babation (The Babolth notation, a Babol is {10,10,100,7 (1) 2}), Treebation (The Treebolth notation, a Treebol is {10,10,10,100,3 (1) 2}), Trabation (The Trabolth notation, a Trabol is {10,10,10,100,7 (1) 2}), Quadribation (The Quadribolth notation, a Quadribol is {10,10,10,10,100,5 (1) 2}), Quintabbation (The Quintabbolth notation, a Quintabbol is {10,10,10,10,10,100,3 (1) 2}), Gootration (The Gootrolth notation, a Gootrol is {10,100 (1) 3}), Booquadrol (The Booquadrolth notation, a Booquadrol is {10,10,100 (1) 4}), Gietration (The Gietrolth notation, a Gietrol is {10,100,5 (1) 3}), Gooquintation (The Gooquintolth notation, a Gooquintol {10,100 (1) 5}), Gissation (The Gissolth notation, a Gissol is {10,10 (1) 100,2}), Mossation (The Mossolth notation, a Mossol is {10,10 (1) 10,100}), Mussation (The Mussolth notation, a Mussol is {10,10 (1) 10,100,5}), Beesation (The Beesolth notation, a Beesol is {10,10 (1) 10,10,100,4}), Treesation (The Treesolth notation, a Treesol is {10,10 (1) 10,10,10,100,4}), Dutration (The Dutrolth notation, a Dutrol is {10,100 (1)(1) 3}), Xappation (The Xappolth notation, a Xappol is 10 by 10 array of 10's), Colossalplexation (The Colossalplexianth notation, a Colossalplex is colossal x colossal x colossal array of 10's), Ectossation (The Ectossolth notation, an Ectossol is the value of a size 10 hexeract (six dimensional cube) of tens), Dimendecation (The Dimendecalth notation, a Dimendecal is 10x10x10x10x10x10x10x10x10x10 array of 10's), Trilatration (The Trilatrith notation, a Trilatri is {3,3 (0,3) 2} = {A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A} where A represents "3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3" - this is a size 3 - x^3x array of 3's), Bongulation (The Bongulusth notation, a Bongulus is {10,100 (0,0,1) 2)), Trongulation (The Trongulusianth notation, a Trongulus is {10,100 (0,0,0,1) 2}), Goppatothplexation (The Goppatothplexianth notation, a Goppatothplex is {10,goppatoth,4} array of 10's), Quadrunculation (The Quadrunculusianth notation, a Quadrunculus is {10,100,4} & 10 = 10^^^^100 array of tens), Golapulusplexation (The Golapulusplexianth notation, a Golapulusplex is a * "10^100 array of tens" array of tens* array of tens), Wompogulation (The Wompogulusianth notation, a Wompogulus is 10^10 "100th level" exploded array of 10's), Meamation (The Meameamealokkapoowath notation, a Meameamealokkapoowa is {L100,10}10,10) and so many other possible notations. You could even take the patturn these numbers are going by and continue the recursion by their own array then have this array go by as much as the largest number, after this take what was just done and the orginal list and count them as twosteps and continue this patturn for the last number in this list number of times and even continue that patturn of building numbers for that number of times. Because Exponentiation, Tetration and Pentation are notations this means that there can be notations so higher that they are notations that need and exponent for themselves and even Tetrate themselves causing a second level of Exponentiation and Tetration. After this this second layer of notations can get so high that they need and exponent starting a third layer of Exponentiation and so on. Building layer after layer there can become enough layers that there needs to be an exponent to represent the number of layers and even a Tetration from them. You could count regular notations and what was just described as two notation dimentions and add enough notation dimentions to need an exponent for them interestingly. This is not just a bunch of random numebrs or even operations, these really could be done.

It just gets confusing when tracking the notations levels and amounts. In a weird sense this leads to a recursive paradox because you end up first: having layers of mathematics as you get with higher numbers the first layers being regular numbers like 1, 2, 3, 4, then you have operations like Addition, Multiplication, Exponentiation, Tetration, then you have notation levels like a notation so high that you need an exponent for that, then a Tetration of operations, a Pentation of operations untill you get into another layer you could call the poetic layer of mathematics where you deal with msotly words and almost never deal with actual numbers. From these four layers you could take this patturn and say instead of 4, 10 or 27 mathematical layers have a Tetration of mathematical layers, then a Tetration of operations of these layers untill you get into the peotic realm, this would make a second set of mathematical layers or a hyper layer and this could continue untill you get into 10, 20 or 10,000,000,000 hyper layers of mathematics starting a recursive paradox of mathematical concepts and higher and higher layers and representative notations. This would almost cancell out mathematics as we know it because the recursive paradox would be beyond number or proper quantities and leak into the peotic descriptions of them.Ironically almsot all of this depends on a lienar coordiante ssytem of mathematics and this could be applied in a 2D, 3D, 10D or a coordiante ssytem with a Tetration of dimentions meaning it invovles so many dimentions that it needs several layers of exponent, then it could be in a coordiante ssytem that invovles a Pentation of dimentions, a Hexation, a Hectation, a Yattation, a Tredation, a Trigination, a Nongentation, a Eightation, a Googolnonaplexation or a Treebation of dimentions, what could be determined from the joined axises of so many dimentions that it needs a Treebation or so many dimentions that it requires a peotic array of numbers transcending real numbers. What was just described would invole a second layer of mathematical dimentions because it is now a set of dimentions each a coordinate ssytem that is a positive and negative array of operations. The dimentions just described could have negative numbers making this a form of altra dimention because it would be an exist with a positive and negative side. This could go into not just one altra dimention but so many altra dimentions that they require a Tetration, Zettation and Zalation of dimentions bacause there are so many to make coordinates with. This would make a third layer of dimentions now imagine based on this building up that there were so many layers of dimentions that they needed a Tetration, Xappation or a peotic array and say that the regular coordinate system of positive and negative operations was one super layer of mathematical dimentions and what was just done was a second super layer of mathematical dimentions. Then create another super layer from that, after all of this take what was done so far, what number would be at the end, not what peotic array, operation but actual number as in just 3, 6, 9, 7, what actual number would be at the end of all of this take that number and what was done in this whole explaination and continue it for as many more steps as the highest number and continue that for as many more steps as the highest number from that and continue that for that many steps and take this whole thing and continue it for a recursive number of times.

Eventually you get stuck because you just keep making each new number a product of the number of steps from the highest number before that and that would be from the number before that, this would simply create a strong of recursion and would need some kind of recursive freedom to get away from this patturn and make other levels of recursion from these. What was described would be the first level of recursion but the second level could be take the patturn of all the numbers in a sequence so and advance that for ([ Take the patturn that was done so far and project it for [ Take the patturn of the numbers descibed before and project then for [ Take the patturn of the numbers decribed before and project them for [ Take what was done on the patturn of numbers before and project them for that many times more. ] many times more. ] many times more. ] number of times more ]take what is represnted in the levels of parenthesis and extend that for that many peranthesi levels what the number happens to be in any sequence like this project it to that conclusion. ) numbers of steps more and what number would you get after that. What was just done could be the second step breaking a simple recursive line and there could be more steps after these. A possible third step although this would not be exact could be take the patturn of the numbers before and continue the patturn for {step2...to steo 2....step 2} continue the patturn so far for {step2...to steo 2....step 2} continue the patturn so far for {step2...to steo 2....step 2}...........for that number of steps more {step2...to steo 2....step 2} this is what step 3 would roughly be. Thank you for this.
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:iconffaat:
ffaat Featured By Owner Oct 2, 2011
Nice!
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