# Hilbert Curve Sierpinsky, Triangle Euler's Spiral (Clothoid), Releaux Triangle..

Has somebody here for these 4 curves

Hilbert Curve, Sierpinski Curve (Triangle), Euler’s Spiral (Clothoid),Releaux Triangle

a numerical solution? The target is to plot the curves in a lcd, or (perhaps

it looks like better) with the help of jit.gl

thank you for serious solutions

hey, i don’t think that will help you a lot but here’s one approach to draw a sierpinsky triangle in an lcd

**all**of the following text. Then, in Max, select

*New From Clipboard*.

```
----------begin_max5_patcher----------
1166.3oc0Z1skaZCDG+Z6mBc31tcq9.ID4t9bzSO4fMJNjhABfS2zbx6dEiv
d8lZLBWqI6di8QfVwvOOy+YFo8aqWEso9ISWD4cj+frZ02VuZEbogKrZb7pn
8YOssLqClVTk4uq27onGb2p27TOb4x5r78ltNB63spOzWZ56+Ziws7QQj+b7
VE4veicc903iS+C0U8UY6gIG86sEYkGuS0g8EU1kBd9ryldWw+.SmwejNd4l
r9sernZ26aMa6cOWMkZuMId3ijgYR31KbxVrqtyRcK+vE+950Ce7v+ehrIqZ
2j7.t4kXhH3LgQU5ARHRAfnnuEvBGMrvoAiJCwHY6L+GrPIRJcYgNZ4BABew
.IIF3AKUAgPLXfFC2j15CU4KiGIrfyCFUl7nzF2vNCH3D2bK.gFbfnUreR73
2H7GmDGevpxzeQlnzXwDtSaUvgAnvjeYRfTTMANRQCGN4TLwws5hjflNBWqe
C3inviGRUv3Qe8tckmR71j0ZeQ5Msu2TksoDrQ5RISr3pEdboDptJPietJCb
9U+y12015qTb9jUcEG9rpiPQ.eJ03QkdxFxlqijGtFZnAuhTUBfiwp0imAM7
6GZNT0js8utpVwCSGXHBes5GSqvbAToA.MSUqtsR8kWstH7wQ5DP2j4DQkwA
nZ8oPBWRIKEHgu5zDM3VvbgOAo8kMG56qqtglYSVZpiTs9kYMdinRxkHz294
TASYxAQRRmouo3ISIwFCXKgQRVbr.eoaClZ4hCbWPfa2vXwB7bf5.zvHb+bh
N66KCqklbI9l22CGyjoyTNZLlBGrkJbnR4+bDNZypxq2SDKtiCVBV6rkaisT
AYeKNreio8l623ZRpLU3kTY7QgBPMURCglZ.IDFIcDpfSnqFXcsZPmLzRD9l
4GccjfrShDcAmahKbD1jCmCS.4xTkm2jYeuapK+JA5bg.kqSF6igbCcyvvXu
1GKa+XJKIh8yrszj0tviiI74rb9OwNAGQR.3Q41oOigxhNPz832iZvW1+ftz
pTNVepqXEoqLU3KOJ5Blh0vp9wyxFdPCW+kuyc0GZ2d78Z7XnIO+fxMc8EUY
8E1BzNaNhWLoOVjmapNOKUdQ2PhKfBzKBeeMGgGlyPHHRlSLyG7Pwyd7gOw3
wGtGlyPC+HYNCGL7r1ifim83i2LddOI93MObnG1VVm1d1Wj2Tak.6NksJws4
CtcYhlJfCF8kC4tb+LpldZ3yFBtugC64.giCwo9P7zkQbcByAbHSQJU4384i
FONIsN9znPPapuzlgBsAPNKs0nEuo7I9OAu3eUhO1CdYO.olY+8BuzGwd6OS
8OZUoc+iynginPKddT.hHg2.1bYbvinBtu5eHZOLex.hj8vtGEr7i4Gztbst
CEaLaALJ.dbB5qqRt39nwwk3YORehHE3ZOyVSJh+dE+5pFYtOJVZIt1Cet3K
Ft1yb9yBD+85UVG5LuzevK9hotG87cGsG48nin6n830NNgWEALezeX3o+vXg
Te1s8kYMMewz1MtlfoDsO6S0smNveaINUtgvJF0Z9Rww4KWOrZee8+Fyj9NI
-----------end_max5_patcher-----------
```

thank you for this 1st hint

one suggestion: is it also possible to use this algorithm to drawing the triangles like an oscilloscope?

this would be more useful for my project

thanks

not sure what you want to do with an oscilloscope, but here are recursive versions of sierpinski and hilbert.

i thinks it’s a pain doing recursions in max, so i chose js for this.

###### Attachments:

sure in max to do recurcions is difficult,

these curves, figures deals as a source to control several parameters -

the "scope" is only a kind of an "indicator"

and; perhaps using of jit.gl could be one choice

to show 3D figures, torus etc

but again: for what I’m looking for is this:

the triangles (in hilbert) should only be "outlined" in the lcd like a lineto command

the coordinates (x,y) of the lined triangles deals as source for parameters

Peter Elsea shows how to make a Sierpinksi Triangle using LCD in one of his great Max tutorials:

ftp://arts.ucsc.edu/pub/ems/maxtutors/advancedMax/Max&Chaos.pdf

He is plotting points rather than using lines.

thank you for this hint William,

the symmetric variant of Sierpinki’s Triangle could be a useful choice

what else about with Euler’s Spiral (Clothoid), Releaux Triangle?

have somebody here some solutions?

btw: I’m looking else for a practicable solution of a chu-attractor

of course, I know that examples. of Lorenz, Roessler exists under MaxMsp

to the Hilbert Curve, Sierpinski Triangle:

which modus is useful to get the recursive coordinates of these curves etc

the target is to output the "lined way" as a list etc

or better unpacked to x, y (and: for 3d curves as z values)

thanks for further help and suggestions

after some time: exists an example (javascripts are also welcome) for the following curves, phenomenas etc

eulers spiral (clothoid)

reuleaux (correct spelled now) triangle and other polygons

minkowski space

mach’s cone

conical spiral

concho spiral

chua_attractor

maxwell-bloch equation (or oscillator?)

maxwells demon

nordstrand

elliptical-, figure8-, standard-torus

planet orbiting in a binary star system

van der pol oscillator

another question: exists a solution to include the scripts by jsxgraph into the MaxMsp environment?

thanks for hints and suggestions

related to this topic:

has somebody a suggestion or solution what are the rules to using an integral (the euler’s spiral, clothoid, cornu need this) in MaxMsp?

some new phenomenas, curves what I’m looking for has been added here

eulers spiral (clothoid) cornu

devils staircase (cantor function)

koch curve

reuleaux triangle and reuleaux polygon

minkowski space

mach’s cone

conical spiral

concho spiral

chua_attractor

maxwell-bloch equation (or oscillator?)

maxwells demon

nordstrand

elliptical-, figure8-, standard-torus

planet orbiting in a binary star system

van der pol oscillator

thanks for your help and solutions

Hi Tst

Did you finally find the way with the eulers spiral?

V. Böhm gave me some suggestions, you could him send a pm to solve your problem

TSt

before i answer the private messages individually, i rather send an example to the list (oh, sorry, forum).

so here goes an implementation of euler’s spiral (clothoid) in a JSUI.

you can also get some interesting artefacts when using extreme values.

###### Attachments:

in the next time I’ve been looking for a solution to output the corners of hilbert and sierpinski as MIDI-Messages e.g.

I’m agree with Volker Böhm that the using of js could be a step to realize this

thank you for help and solutions

now after few weeks ago I repeat this:

exists a solution to output the corner-points of hilbert and sierpinski as MIDI-Messages e.g.?

thanks

@V.Böhm

after some time, we need now a variant for sierpinski, hilbert or similar fractals but more a recursive output by the knots (gemeint sind die Eckpunkte welche als x,y Paare weiterverarbeitet werden sollen) btw, not only the variant as code but also a patcher under MaxMsp could be useful

thx and happy maxing