Magic color: Ghost constructions

rafael shared this question 9 years ago
Answered

Hi,

Dynamic Color can be used easily as a powerful tool to discover unknown loci, just knowing the condition to be satisfied by each point.


Steps:


A=(2,-1)

B=(10,-3)

C=(8,2) (Trace On)

a=Segment[A,C]

b=Segment[B,C]

goal=10 (slider)

condition=(a+b)/goal

Dynamic Color to C: R = G = B = condition

Move C! (ghost: ellipse)


ellipse


goal=5

condition=(a-b)/goal

Move C! (ghost: hyperbola)


hyperbola


goal=16

condition=(a b)/goal

Move C! (ghost: Cassini oval)


Cassini


Of course, the condition can be much more elaborate. In addition, instead of gray color can easily obtain. For example:


Mandelbrot


Mandelbrot_detail


All the Best,

Rafa

https://ggbm.at/540081

Comments (15)

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1

Hi Rafa


Excellent :D

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1

hola rafael

esto es una maravilla

ya estoy pensando en fantasmas de inecuaciones

pero, por supuesto, que se animen automaticamente

espero que te mejores de tu más que previsible tendinitis dactilar

lo traduciré debajo con un traductor para que no digan que aquí se habla inglés


saludos


translated with REVERSO:


Hello Rafael this is a marvel

already I am thinking about ghosts of inequations

but, certainly, with automatic animation

I hope that you get improved of your more than predictable finger tendinitis


Regards

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1

Hi


After more than 3 hours:


3b3db34517eda4e9213276c5cd579751


https://ggbm.at/540109

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1

Really beautiful :D :exclamation: :exclamation: :exclamation:

Rafa

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hi


In the zzz.ggb file, instead 20 iterations A1,..., A20 I made 100 iterations A1, ..., A100. After 4 hours, the result was this:

d514dd15856a0f3b0390f055ee149ce9

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1

:D Other four hours... without random :D


zzz_z

https://ggbm.at/540117

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1

Rafa,


!magnífico, increíblemente hermoso!


Kathryn

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Ola Rafa

Waiting 4 hours can be a pleasure :D

Bravo

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1

Hello!

I like very much your construction - by the way that reminds me the programing on our old Commodore C64 after reading about the Mandelbrot set in Scientific American in 1986.... Anybody remembers those times?

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1

Yes, me, for example

And 64 KB was an eternity ... :-)

Greetings to the GI of Warsaw!


Saludos,

Rafa

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1

Hello (again) :)


I've found a method to create this "color mapping" very fast, in seconds. You can see a very simple example in:


http://www.youtube.com/watch?v=Uj2K_-0gPxQ


Basically, the technic consists use spreadsheet to copy fastly the Dynamic Color property to 300 or 350 points. It's enough construct of the first row of the spreasheet and then copy all the rest.


Depending on the computer, you may need to change the speed slider to get a "clean" scan.


See attached for details (it's better to see first the scannner.ggb file).


Best Regards,

Rafael Losada

https://ggbm.at/544677

https://ggbm.at/544679

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1

Hello (again) :)


I've found a method to create this "color mapping" very fast, in seconds. You can see a very simple example in:


http://www.youtube.com/watc...


[...]


Best Regards,

Rafael Losada


Che meraviglie!


Ciao

Renata

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hello

this method will graph beautiful inequalities


te veo en forma rafa

saludos

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Thank you, Mathmagic.


Yes, the method can get any map if we can construct the conditions of only one point in the first row of the spreadsheet.


Saludos,

Rafa

PS: También te veo en forma :-)

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Bjr, Noel


Yes, a nice (arab? :D ) example!


Best,

Rafa


01

https://ggbm.at/544959

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