Find other swords down the waterfall

Question

This is another old pattern I generated with a 1D cellular automaton:

To me it looks like a sword hidden in a waterfall.

The neighborhood of a cell looks like this:

What is the rule behind this pattern?

Find at least one other sword down below and show what it looks like.

Edit The last part of the question doesn't really fit, so I accepted the first answer, stating the rule. I will post the pictures of other 'swords' mysefl to show what I meant. The title of the question can be interpreted figuratively now, only meaning 'find the rule to generate the pattern further'.

Btw, this is what I meant by 'other swords':

Answer 1

I'm not sure how the rules are written but it seems to be either

2nd generation alive with no first generation

or

A number of 1st generation alive with no second generation (100,010,001,101,111)

Image

Red is dead

Answer 2

This is based on gtwebb's answer, so please don't treat this as an answer in its own right.

Quick and nasty Microsoft Excel VBA code to generate image:

Sub RunIt()
    Application.ScreenUpdating = False
    Dim r As Long
    Dim c As Long
    Dim cnt As Integer
    Cells.Interior.Color = xlAutomatic
    Cells(2, 8000).Interior.Color = vbRed
    r = 3
    Do While r < 500
        For c = 8000 - r To 8000 + r
            cnt = 0
            If Cells(r - 2, c + 0).Interior.Color = vbRed Then cnt = cnt + 4
            If Cells(r - 1, c - 1).Interior.Color = vbRed Then cnt = cnt + 1
               If Cells(r - 1, c + 0).Interior.Color = vbRed Then cnt = cnt + 2
               If Cells(r - 1, c + 1).Interior.Color = vbRed Then cnt = cnt + 1
               If cnt = 1 Or cnt = 2 Or cnt = 4 Then
                  Cells(r, c).Interior.Color = vbRed
            End If
        Next
        r = r + 1
    Loop
    Cells(1, 8000).Select
    Application.ScreenUpdating = True
End Sub

First 500 iterations (generated while the VBA code was working sideways - the code above has been modified to work downward):