Magic color: Ghost constructions

rafael shared this question 14 years ago

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)

goal=5

condition=(a-b)/goal

Move C! (ghost: hyperbola)

goal=16

condition=(a b)/goal

Move C! (ghost: Cassini oval)

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

All the Best,

Rafa

https://ggbm.at/540081

1

Hi Rafa

Excellent :D

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

but, certainly, with automatic animation

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

Regards

1

Hi

After more than 3 hours:

https://ggbm.at/540109

1

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

Rafa

1

hi

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

1

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

https://ggbm.at/540117

1

Rafa,

!magnífico, increíblemente hermoso!

Kathryn

1

Ola Rafa

Waiting 4 hours can be a pleasure :D

Bravo

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?

1

Yes, me, for example

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

Greetings to the GI of Warsaw!

Saludos,

Rafa

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:

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,

https://ggbm.at/544679

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:

[...]

Best Regards,

Che meraviglie!

Ciao

Renata

1

hello

this method will graph beautiful inequalities

te veo en forma rafa

saludos

1

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 :-)

1

Bjr, Noel

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

Best,

Rafa

https://ggbm.at/544959