# Talk:Barnsley fern

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Field:  Geometry

## Untitled

nice article - well done Victuallers (talk) 14:29, 19 January 2010 (UTC)

## Suspect a small error?

" ... Barnsley's fern uses four affine transformations. The formula for one transformation is the following: ..." Uhh, to my limited mathematics, the formula is the same for all four transformations. The difference between them is the factors in the matrix (abcd values). The sentence should therefore read: " ... The formula for the transformations is the following: " Old_Wombat (talk) 11:07, 15 May 2011 (UTC)

Formula is different for each of 4 transformation. We can talk about general transformation with named coeeficient, but this is just abstract thing. Concrete transformation have concrete coefficients. So, there is no error in article. — Preceding unsigned comment added by 91.213.255.7 (talk) 00:28, 10 September 2011 (UTC)

Uhh, having redone the program, I am sticking to my guns. The formula IS the same, it merely has different coefficients. I even coded it that way in my program - same formula for all, select different a-f values for different probabilities. Even the vertical "stalk" is in fact a "frond" with zero width (a = 0 in the f1 column). Old_Wombat (talk) 23:10, 16 December 2012 (UTC)

## Explanations of Transforms are Wrong

The explanations of how the particular transforms map things (in the "computer generation" section) are entirely wrong, other than the first one (the stem). The second one maps the fern onto a slightly smaller copy of itself that is moved upwards from the base and rotated slightly -- that is, it creates the second pair of leaflets from the first, the third from the second, and so on up the fern. The third one maps the whole fern onto the left-hand leaflet (thereby creating that leaflet as a much smaller copy of the whole fern), and the fourth one does the same from the right-hand leaflet. Critical errors are that the leaflets are described as copies of other leaflets rather than copies of the *whole* fern -- which is necessary in how affine transform fractals work; they cannot transform only a portion of the whole! -- and that the description of the second transform is actually approximately correct for the *third*. Sorry I don't have time to make the corrections myself. 64.81.73.35 (talk) 02:57, 8 October 2011 (UTC) agree, the explanation is not right. F2 moves the current point up and to the right, staying on the same side of the major stem. F3 relocates any point, anywhere on the entire leaf, back to the bottom left leaf, and F4 to the bottom right leaf. The leaves above the bottom left/right leaves are partial copies of the bottom leaf, depending how many consecutive F2s run. 104.5.42.186 (talk) 19:14, 9 May 2015 (UTC)

## More info and a correction for the second example.

If you look at the larger image of the second fern ("Mutant Varieties"), you can see that the horizontal "stalks" actually go a little bit past the vertical "stalk" (fractis). On a 1280 X 1024 screen, this is even more startling. A better results is obtained with a slightly different value of the first 'd' parameter (in the "f1" row) : 0.07 instead of 0.25 . This matches up the stalks to within a pixel or so on the 1280 wide screen.

Also, with the second fern, the range of values is completely different. Measuring them empirically in single precision with ten million iterations, I obtain the following: -1.485 < x < 1.473 and -0.431 < y < 7.088 . The vagaries of the Microsoft random number generator (and possibly rounding errors within the single precision calculations) have these vary by a fraction of a percent or so between simulations, even with ten million iterations.

Now all of this is, of course, OR, so it can't go into the main article, but in the spirit of improving articles I present it here. If someone else can run the simulation and can confirm these results, then maybe this information can progress into the main article. Old_Wombat (talk) 23:05, 16 December 2012 (UTC)