cKleinhuis


« on: September 22, 2014, 10:59:54 PM » 



« Last Edit: September 23, 2014, 12:31:18 AM by cKleinhuis »

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Aexion


« Reply #1 on: September 23, 2014, 01:25:55 PM » 

Beautiful videos! They explain the whole concept of the complex multiplication symmetry very well!! Many Thanks! (Now I'm thinking in angular folding.. )


« Last Edit: September 23, 2014, 01:31:38 PM by Aexion »

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cKleinhuis


« Reply #2 on: September 23, 2014, 01:44:40 PM » 

thank you for the comment, i think it is really good occasion to explain that, for once it bugged me all the time understanding the symetries, but when looking at the result and the point movements from the 2 different folds it became just obvious although my comments seem to be quite rusty i think the visualisation makes up for it lol always nice that at least one dude appreciates what i do



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cKleinhuis


« Reply #3 on: September 23, 2014, 01:46:28 PM » 

Beautiful videos! They explain the whole concept of the complex multiplication symmetry very well!! Many Thanks! (Now I'm thinking in angular folding.. ) i am more thinking to adjust the burning ship folding operation with a distance similar to the one used in the mandelbox, param value=0 is normal abs() like fold, but param value=1 would fold on the 1 line, since the abs() is so related it would make sense to have an adjustable parameter here



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Aexion


« Reply #4 on: September 24, 2014, 12:30:48 AM » 

thank you for the comment, i think it is really good occasion to explain that, for once it bugged me all the time understanding the symetries, but when looking at the result and the point movements from the 2 different folds it became just obvious although my comments seem to be quite rusty i think the visualisation makes up for it lol always nice that at least one dude appreciates what i do Your visualizations are very good and it shows very well the whole process!! Someday, if you have spare time, try to visualize the Newton fractal.. i am more thinking to adjust the burning ship folding operation with a distance similar to the one used in the mandelbox, param value=0 is normal abs() like fold, but param value=1 would fold on the 1 line, since the abs() is so related it would make sense to have an adjustable parameter here It's an interesting idea, two folding lines, one real and the other imaginary.. I'm just toying with the idea of the angular fold, to see how it looks..



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cKleinhuis


« Reply #5 on: September 24, 2014, 12:50:56 AM » 

Your visualizations are very good and it shows very well the whole process!! Someday, if you have spare time, try to visualize the Newton fractal.. It's an interesting idea, two folding lines, one real and the other imaginary.. I'm just toying with the idea of the angular fold, to see how it looks.. what do you mean by angular fold? take a bias and flip them around that ? e.g. bias 90° 45 becomes 135° and vice versa? newton fractal: i am going to cover basically everything BUT one step after another, the newton uses the inverse bailout which needs a special explanation, next is to visualise some minibrots and miniburning ships which is quite interesting as well, and after that i hope to have the time to finish the long planned julia explanation, because the julias explain why the mandelbrot iterations starts at that point 0,0 i think complex division will need another short explanation as well ( multiply by inverse )



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cKleinhuis


« Reply #6 on: September 24, 2014, 01:02:33 AM » 

and furthermore, the newton is complicated in the way the braces work in the formula its not the division, but i need to adjust the visualisation, because the "z" value is transformed in 2 different ways before divided with each other, i am aware of it for a long time, and it could be done with a branching movement but i am not content with the outcome because it would look veeeery messy and the exponentiation with an always changing exponent is even more confusing, lol i am quite unsure if it can be done in a way that provides insight, one way could be to keep the points that move away from one single z (divisor and dividend) could be connected so that one can at least follow which point is divided by which  quite a good idea nice i try that
but i will certainly work on something like that, especially because i want to generalise the visualisation even further and visualise the process of fluid dynamics because the navier strokes equation is an iterative process as well ( and hence fractal in its most basic form, aside of the fluid dynamic result coming out of it ) , and i want to help people understanding the navier strokes equation (lol although i have never understood it myself, or because of that ) so, it is an ever ongoing process but i am certain in one way or another more complex formulas can be easier understood if it is visualised what they actually do and what problems occur in higher iterations... lol *mad laughter*


« Last Edit: September 24, 2014, 01:06:16 AM by cKleinhuis »

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Aexion


« Reply #7 on: September 24, 2014, 01:41:58 AM » 

what do you mean by angular fold? take a bias and flip them around that ? e.g. bias 90° 45 becomes 135° and vice versa?
Yes, It's just an idea.. imagine that you set an angular window between 30º and 30º.. any point whose angle falls inside this window is unchanged.. if a point has an angle of 40º, then it will be fold to 20º (the radius is unchanged).. same happens if a point is for example, 50º.. since the nearest pivot is 30º, then it's folded to 10º.. When you use abs(x) and abs(y) you use a fold window between 0 and 90º.. but if you plan to use other angles, you need to get the point angle and radius first.. then change the angle and calculate the new point with the radius. oh well, it's just an idea and need to implement it.. newton fractal: i am going to cover basically everything BUT one step after another, the newton uses the inverse bailout which needs a special explanation, next is to visualise some minibrots and miniburning ships which is quite interesting as well, and after that i hope to have the time to finish the long planned julia explanation, because the julias explain why the mandelbrot iterations starts at that point 0,0 i think complex division will need another short explanation as well ( multiply by inverse ) Complex division it really needs a visualization. It's not easy to understand..



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cKleinhuis


« Reply #8 on: September 24, 2014, 01:55:55 AM » 

Complex division it really needs a visualization. It's not easy to understand.. it has to be introduced with a simple divident, like ^2 for multiplication, ^0.5 would serve that, just halving distance and subtract angle by 1/2 ... both of the transforms (mul and div, i now they are the same but the show is about explaining most simple stuff, and division and multiplication is observed as different operation, perhaps i can manage to include an explanation that they are "just" reverse to eachother like +/ including a neutral element and completing the space lols ) can get very confusing when used with other multiplicants/dividents so, point me to a simpler fractal to handle beforehand, i was thinking of the "nova" but before that the "manowar" because this one needs to keep track of the previous location (visualised by lines that stay connected)


« Last Edit: September 24, 2014, 01:59:26 AM by cKleinhuis »

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mclarekin


« Reply #9 on: September 25, 2014, 03:01:44 AM » 

lol always nice that at least one dude appreciates what i do As unofficial spokesman for the silent majority, we all appreciate what you do. We are just very silent about it The visualisations are impressive and informative. thanks.



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cKleinhuis


« Reply #10 on: September 25, 2014, 03:22:36 AM » 

As unofficial spokesman for the silent majority, we all appreciate what you do. We are just very silent about it The visualisations are impressive and informative. thanks. appreciated, thanks, since one already stated  i am already working on the next issues



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