I'm fascinated with fractal mathematics

>The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/)[1][2] is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0}, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.[3]

sources:

man fraqtive(1)

https://en.wikipedia.org/wiki/Mandelbrot_set

#mathematics #advanced #programming #Lineair #Algebra #complex #numbers #matrix #technology #mandelbrot #fractals #OpenSource

mandelbrot 14:13

syntax

• fraqtive
• type mandelbrot
• parameters normal
• generation 2D

definitions:

The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/)[1][2] is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0}, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.[3]

sources:

man fraqtive(1)

https://en.wikipedia.org/wiki/Mandelbrot_set

#mathematics #advanced #programming #Lineair #Algebra #complex #numbers #matrix #technology #mandelbrot #fractals #OpenSource

mandelbrot 14:11

syntax

• fraqtive
• type julia
• parameters normal
• generation 2D

definitions:

The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/)[1][2] is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0}, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.[3]

sources:

man fraqtive(1)

https://en.wikipedia.org/wiki/Mandelbrot_set

#mathematics #programming #advanced #Lineair #Algebra #complex #numbers #matrix #technology #mandelbrot #fractals #OpenSource

mandelbrot 14:05

syntax

• fraqtive
• type mandelbrot
• parameters normal
• generation 2D

definitions:

The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/)[1][2] is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0}, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.[3]

sources:

man fraqtive(1)

https://en.wikipedia.org/wiki/Mandelbrot_set

#mathematics #programming #advanced #mathematics #Lineair #Algebra #complex #numbers #matrix #technology #mandelbrot #fractals #OpenSource

So the #mandelbrot set is connected, because there is a one-to-one (conformal) mapping f(p) between its complement and the complement of the closed unit disk.

Has anyone made an animation of the Julia set of f(p(t)), where p(t) goes around the unit circle?
(i.e. p(t)= (1+ε) · e^(2πit) for some small positive number ε)

#fractal