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Author Topic: Re: Custom formulas & transforms - Release  (Read 3592 times)
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jim373
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« on: February 07, 2011, 02:31:00 PM »

Thank you Luca! I am looking forward to trying out your new formulas!  grin
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KRAFTWERK
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« Reply #1 on: February 07, 2011, 02:41:17 PM »

Me too!!  afro
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Madman
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« Reply #2 on: February 07, 2011, 07:34:20 PM »

I'm hardly keeping up updating M3D jabbering

The next challenge will be finding time to test them...

But nevertheless: Keep them coming Darkbeam!
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Jesse
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« Reply #3 on: February 07, 2011, 07:45:13 PM »

I'm hardly keeping up updating M3D jabbering

And i thought i would be the only one  rolling on floor laughing
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DarkBeam
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« Reply #4 on: February 07, 2011, 08:37:11 PM »

I'm hardly keeping up updating M3D jabbering

The next challenge will be finding time to test them...

But nevertheless: Keep them coming Darkbeam!


Surely do :lol:
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zongo
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« Reply #5 on: February 09, 2011, 08:47:25 PM »

Thank you so much for sharing those formulas with us Darkbeam !
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richardphotos
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« Reply #6 on: February 14, 2011, 12:28:46 AM »

thanks for all the hard work all of you do and especially to Jesse
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MarkJayBee
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« Reply #7 on: February 16, 2011, 07:37:39 PM »

Many thanks for all these fascinating new Adds Luca.
Just have to find some time now to explore them properly!  wink
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ericr
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« Reply #8 on: February 19, 2011, 06:49:03 PM »

Can you make a newton formulas
 z= z- f(z)/f'(z)  Z in Complexes or Z in quaternions
Tank you
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #9 on: February 19, 2011, 07:37:22 PM »

Can you make a newton formulas
 z= z- f(z)/f'(z)  Z in Complexes or Z in quaternions
Tank you

Too bad Newton formulas are not convergent so they won't work properly for this program. sad
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ericr
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« Reply #10 on: February 22, 2011, 05:05:36 PM »

 Can you make a formula like Z power q +c but q in Quaternions q=a+ib+jC+kd
a,b,c,d in Real
Thank you for all you done





« Last Edit: February 22, 2011, 05:09:27 PM by ericr » Logged
DarkBeam
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« Reply #11 on: February 22, 2011, 06:13:34 PM »

Can you make a formula like Z power q +c but q in Quaternions q=a+ib+jC+kd
a,b,c,d in Real
Thank you for all you done

My dear I was planning to do this but I fear this is far too complex and almost useless. Why?
2D fractals with complex powers are all weird looking, because complex part of the power screws up the shape making it non-symmetrical. I have never (never!!!!) seen a fractal with a complex power in any artistic site. So why try to extend this in quat? A really hard work for nothing - nobody will ever use this. If you need to raise a quat to a neg power (-1) you can use sphereinv that already gives beautiful results. I will extend that transform soon. Also, raise to a fractional power is useless due to non-symmetry. sad

raising quat to a quat power;

a ^ b = exp ( b log(a))

1 step: calculate the log of the x,y,z,w quat. It requires four calculations, each one with four + four terms. You cannot do this saving variables at each step but saving at the end undecided a lot of time to write and very error-risky! I don't have the log fmla already written, so I should write it by scratch! Ouch!!! (well, probably it will require even more steps. I am making an optimistic prevision grin )
2 step: Multiply by the quat containing bx,by,bz,bw. I fear this is almost impossible without using additional storing bercause fp stack size is only 8 and I cannot exceed it! I must do all computations and then save
3 step: calculate the exp of the previous quat. Other very hard step.
4: Assign previous values to w,z,y,x... easy smiley

Another transform that I wish to do is Mobius in 4D; but I am not able because I need more than 4 slots and I don't know how to do! sad

Please for now use what is already done... Azn
« Last Edit: February 22, 2011, 06:18:33 PM by DarkBeam » Logged

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DarkBeam
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« Reply #12 on: February 22, 2011, 06:26:20 PM »

This example: Mset raised to .5 power.

Useless, because the formula is discontinue and fragmented (like Barnsley but less regular) sad


* aaaaa iko.PNG (147.62 KB, 522x466 - viewed 167 times.)
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DarkBeam
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« Reply #13 on: February 22, 2011, 06:29:53 PM »

Raised to (0,1) power. Still want to extend this crap to quats? wink


* aaaaa iko.PNG (28.12 KB, 620x348 - viewed 160 times.)
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Jesse
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« Reply #14 on: February 22, 2011, 10:14:57 PM »

Another transform that I wish to do is Mobius in 4D; but I am not able because I need more than 4 slots and I don't know how to do! sad

you can use dfree1+2 and deriv2+3 are not used yet:

    Dfree1:     Double;     //+216
    Dfree2:     Double;     //+224
    Deriv1:     Double;     //+232    for 4D first deriv or as full derivs
    Deriv2:     Double;     //+240
    Deriv3:     Double;     //+248
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