[math-fun] What's this fractal's name?
On 2018-12-10 15:10, Mike Stay wrote:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
I just call it (turned CW 90º) the complex base -2 region. (The digits are 0 and the cube roots of 1.) "Proof": Divide it by -2. (= rotate 180º and halve the scale.) Make four copies, displaced by each of the four digits. Form their union, which will be disjoint except at the boundaries. It's ba-a-ack! —rwg
Ah ha! Thank you! With that keyword, I found one of the images I'd seen before in my math-fun archive: http://gosper.org/base-2d.png On Wed, Dec 12, 2018 at 3:25 AM Bill Gosper <billgosper@gmail.com> wrote:
On 2018-12-10 15:10, Mike Stay wrote:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
I just call it (turned CW 90º) the complex base -2 region. (The digits are 0 and the cube roots of 1.) "Proof": Divide it by -2. (= rotate 180º and halve the scale.) Make four copies, displaced by each of the four digits. Form their union, which will be disjoint except at the boundaries. It's ba-a-ack! —rwg
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
Anyone care to add the details to https://en.wikipedia.org/wiki/Complex-base_system ? On Wed, Dec 12, 2018 at 8:02 AM Mike Stay <metaweta@gmail.com> wrote:
Ah ha! Thank you! With that keyword, I found one of the images I'd seen before in my math-fun archive: http://gosper.org/base-2d.png On Wed, Dec 12, 2018 at 3:25 AM Bill Gosper <billgosper@gmail.com> wrote:
On 2018-12-10 15:10, Mike Stay wrote:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
I just call it (turned CW 90º) the complex base -2 region. (The digits are 0 and the cube roots of 1.) "Proof": Divide it by -2. (= rotate 180º and halve the scale.) Make four copies, displaced by each of the four digits. Form their union, which will be disjoint except at the boundaries. It's ba-a-ack! —rwg
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
On Thu, Dec 13, 2018 at 4:26 PM Mike Stay <metaweta@gmail.com> wrote:
Anyone care to add the details to https://en.wikipedia.org/wiki/Complex-base_system ?
No. In light of my experience trying to get Julian's equilateral example <http://gosper.org/dodohedron.png> added to the dodecahedron article, and Henry's experience trying to contribute his cubic solution <http://gosper.org/cubic.gif> animation. It's a shame, because I have a neat idea to animate their twindragon figure: Tile the plane with them, as in AoCPII <http://gosper.org/twindragon.png> , But colored like a checkerboard. Iterate these three commutative transformations: merge horizontally adjacent pairs, with their colors converging to the left one or the right, in a coarser, skewed checkerboard. Rotate cw 135º. Shrink by √2. Net effect: None. —rwg On Wed, Dec 12, 2018 at 8:02 AM Mike Stay <metaweta@gmail.com> wrote:
Ah ha! Thank you! With that keyword, I found one of the images I'd seen before in my math-fun archive: http://gosper.org/base-2d.png On Wed, Dec 12, 2018 at 3:25 AM Bill Gosper <billgosper@gmail.com>
wrote:
On 2018-12-10 15:10, Mike Stay wrote:
I've seen it here on the list multiple times, but can't find it at
the moment.
I just call it (turned CW 90º) the complex base -2 region. (The digits are 0 and the cube roots of 1.) "Proof": Divide it by -2. (= rotate 180º and halve the scale.) Make four copies, displaced by each of the four digits. Form their union, which will be disjoint except at the boundaries. It's ba-a-ack! —rwg
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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Bill Gosper -
Mike Stay