[math-fun] What's this fractal's name?
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
If it doesn't have a name, "Mickey" suggests itself. On Mon, Dec 10, 2018, 6:11 PM Mike Stay <metaweta@gmail.com wrote:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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Mickey Louse? On 12/11/18, Allan Wechsler <acwacw@gmail.com> wrote:
If it doesn't have a name, "Mickey" suggests itself.
On Mon, Dec 10, 2018, 6:11 PM Mike Stay <metaweta@gmail.com wrote:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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This one can be obtained by the L-system with map F |--> F+FF-F with axiom F+F+F where the constants '+' and '-' are turns by +-120 degrees. Helmberg calls the underlying curve (use the axiom F) the "crab" or the "crab fractal". See Gilbert Helmberg: {On the Eisenstein packing of the complex plane}, The Mathematical Intelligencer, vol.~37, no.~2, pp.~27-33, (June-2015). and Gilbert Helmberg: {The Crab: A Connected Fractile of Infinite Connectivity}, Fractals, vol.~19, no.~03, pp.~367-377(?), (2011). It also appears in Gilbert Helmberg: {Getting Acquainted with Fractals}, Walter de Gruyter, (2007). If someone needs much better images of this, just holler (CC personal mail because it is getting increasingly difficult for me to follow math-fun). Best regards, jj * Mike Stay <metaweta@gmail.com> [Dec 12. 2018 15:42]:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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Thanks everyone! On Wed, Dec 12, 2018 at 8:10 AM Joerg Arndt <arndt@jjj.de> wrote:
This one can be obtained by the L-system with map F |--> F+FF-F with axiom F+F+F where the constants '+' and '-' are turns by +-120 degrees.
Helmberg calls the underlying curve (use the axiom F) the "crab" or the "crab fractal". See Gilbert Helmberg: {On the Eisenstein packing of the complex plane}, The Mathematical Intelligencer, vol.~37, no.~2, pp.~27-33, (June-2015). and Gilbert Helmberg: {The Crab: A Connected Fractile of Infinite Connectivity}, Fractals, vol.~19, no.~03, pp.~367-377(?), (2011).
It also appears in Gilbert Helmberg: {Getting Acquainted with Fractals}, Walter de Gruyter, (2007).
If someone needs much better images of this, just holler (CC personal mail because it is getting increasingly difficult for me to follow math-fun).
Best regards, jj
* Mike Stay <metaweta@gmail.com> [Dec 12. 2018 15:42]:
I've seen it here on the list multiple times, but can't find it at the moment. https://imgur.com/a/KeO26Sq
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
A high res image of the fractal rendered using the escape-time method, colourings: Outside = Distance Estimation (could’ve done with using larger bailout) Inside = IFS genetics based https://fractalforums.org/index.php?action=gallery;sa=view;id=1948
On 12 Dec 2018, at 15:11, Mike Stay <metaweta@gmail.com> wrote:
Thanks everyone!
Direct rendering using the IFS corresponding to the numeration system: https://jjj.de/tmp-math-fun/eisenstein-tile.png Radix = -2, digits = zero and third roots of unity, as indicated on top of image. Best regards, jj * D J Makin via math-fun <math-fun@mailman.xmission.com> [Dec 16. 2018 13:41]:
A high res image of the fractal rendered using the escape-time method, colourings:
Outside = Distance Estimation (could’ve done with using larger bailout) Inside = IFS genetics based
https://fractalforums.org/index.php?action=gallery;sa=view;id=1948
On 12 Dec 2018, at 15:11, Mike Stay <metaweta@gmail.com> wrote:
Thanks everyone!
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On Wed, Dec 12, 2018 at 8:10 AM Joerg Arndt <arndt@jjj.de> wrote:
This one can be obtained by the L-system with map F |--> F+FF-F with axiom F+F+F where the constants '+' and '-' are turns by +-120 degrees.
Yes, that's how I drew the one in the picture I'd sent.
Helmberg calls the underlying curve (use the axiom F) the "crab" or the "crab fractal". See Gilbert Helmberg: {On the Eisenstein packing of the complex plane}, The Mathematical Intelligencer, vol.~37, no.~2, pp.~27-33, (June-2015). and Gilbert Helmberg: {The Crab: A Connected Fractile of Infinite Connectivity}, Fractals, vol.~19, no.~03, pp.~367-377(?), (2011).
It also appears in Gilbert Helmberg: {Getting Acquainted with Fractals}, Walter de Gruyter, (2007).
If someone needs much better images of this, just holler (CC personal mail because it is getting increasingly difficult for me to follow math-fun).
Thanks! -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
participants (5)
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Allan Wechsler -
D J Makin -
Fred Lunnon -
Joerg Arndt -
Mike Stay