Re: Standard way to compute a Mandelbrot fractal in APL

[Dr . Jürgen Sauermann]

    Hi Kacper,
      
      thanks, fixed missing DOMAIN ERROR in SVN 1348.
    
    Best Regards,
    Jürgen

On 9/22/20 10:44 AM, Kacper Gutowski wrote:

> On Mon, Sep
>       21, 2020 at 01:17:18PM +0800, Elias Mårtenson wrote:
>       
> > What is the neatest way to compute a
> >         Mandelbrot fractal in APL? The fact
> >         
> >         that you have to break out of the loop as soon as the absolute
> >         value of Z
> >         
> >         is >2 makes it a bit ugly. Is there a neater way to do this?
> >         
> >         
> >         This is what I came up with that works in GNU APL:
> >         
> >         
> >         " #"[⌊0.5+50÷⍨ { (n ⊣ {(x+⍵×⍵) ⊣ n←n+1}⍣{(2<|⍺) ∨ n≥50} n←0)
> >         ⊣ x←⍵ }¨
> >         
> >         (0J1×r) ∘.+ r←¯2+25÷⍨⍳100]
> >         
> >         
> >       
>       
>       If you wanted to use different colors for different number of
>       iterations before it escapes 2≥| disc, my only suggestion would be
>       to get rid of each which makes it slow.  But since you only need
>       one fixed threshold, I would do it like that:
>       
>       
>             rr←(0J1×r) ∘.+ r←¯2+25÷⍨⍳100
>       
>             " #"[⎕IO+ 2≥| {⍺+×⍨⍵⊣((2<|,⍵)/,⍵)←2}⍣23⍨ rr]
>       
>       
>       (⍣23 instead of 25 because I start from ⍺ rather than from 0.)
>       
>       Notably, if you use ⋆ with real right argument instead of ×, GNU
>       APL has a bug where it returns infinity instead of a domain error,
>       so you don't need to check for it ;)
>       
>       
>             " #"[⎕IO+ 2≥| {⍺+⍵⋆2}⍣23⍨ rr]
>       
>       
>       
>       /cc Jürgen:
>       
>       
>             x←2⋆999
>       
>             x⋆2    ⍝ should be a domain error
>       
>       ∞
>       
>             x⋆2J0  ⍝ like it is here
>       
>       DOMAIN ERROR
>       
>             x⋆2
>       
>             ^^
>       
>       
>       -k
>       
>       
>