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Given a chord, I can play its notes in random order (usually fast) for full note's duration. It's not an arpeggio, because arpeggios have ascending or descending order; and arpeggio ends when all its notes have been played. It's not a tremolo, because tremolo is repetitions of a fixed note/chord or alternating of two fixed notes/chords.

So, what is it called and how to notate it? It's very strange if there is no standard way, because I hear such things very often, especially in piano improvisations (it's a good choice for a long final chord, for example).

For myself, I notate it like this:

enter image description here

but I don't know how to notate it in the right way.

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    The definition of arpeggio is not as strict as you think. It's more to describe the texture of how to play a chord which is one note at a time one after another. It's why Alberti bass is considered an arpeggiation even though it's not strictly ascending/descending like the typical arpeggios . – Dom♦ Jul 19 '15 at 15:06
  • As @Dom points out, an arpeggio requires only that the notes not be played simultaneously. There is no restriction on ordering. By "random", do you mean that the notes are played in an order other than strictly from top-to-bottom or bottom-to-top. Or do you intend random to mean played differently (randomly) at each performance? – Nick Jul 19 '15 at 21:41
  • @Nick R, I mean play notes randomly each time until note's duration ends. Like tremolo but randomly play notes instead of alternating. – user15155 Jul 20 '15 at 10:52
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I'm afraid that there is no indication on playing notes randomly. You sometimes have a cadenza but this is just a passage where the performer is given a chance to solo a bit. This is not entirely random though as the performer still has to somewhat stay on theme.

You also have Ad libitum which can be considered "At ones pleasure" This is when a performer is given a certain amount of artistic license in pieces. It can also be considered improvising.

Although these may be somewhat similar to what you claim I would not consider this to be random.

PS that notation you mention makes no sense. You would either have something like this for the arpeggiation

Arpeggio

Or this for a tremolo.

Trem

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In fingerstyle, I often use this with nylon strings and so far (over twelve years of guitar study) I have not seen a notation for it. Thus, I set a figure, double vertical thick line, to use in my sheets and named it as chord-flood. Because feeling of it reminds me flood.

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