Scratch art

by sonone, May 28, 2020, 7:16 PM

I was playing around with circle and the for(...){...} function and got some nice results.
I will post a lot of examples in this post by editing, so don't forsake this post!

$P_i\to P_{i^2}$
$[asy] size(600); dotfactor=1; for(int j=1; j<=4; ++j){ for(int i=1; i<=360/j; ++i){ dot((2*j,0)+dir(j*i)); draw((2*j,0)+dir(j*i)--(2*j,0)+dir(j*i^2)); }} [/asy]$

$P_i\to P_{i^3}$
$[asy] size(600); dotfactor=1; for(int j=1; j<=4; ++j){ for(int i=1; i<=360/j; ++i){ dot((2*j,0)+dir(j*i)); draw((2*j,0)+dir(j*i)--(2*j,0)+dir(j*i^3)); }} [/asy]$

$(\cos x,\sin x)\to(\sin x,\cos x)$
$[asy] size(600); dotfactor=1; for(int j=1; j<=4; ++j){ for(int i=1; i<=360/j; ++i){ draw((2*j,0)+(cos(i),sin(i))--(2*j,0)+(sin(i),cos(i))); }} [/asy]$

$P_i\to P_{(-1)^i2i}$
$[asy] size(600); dotfactor=1; for(int j=1; j<=4; ++j){ for(int i=1; i<=360/j; ++i){ dot((2*j,0)+dir(j*i)); draw((2*j,0)+dir(j*i)--(2*j,0)+dir((-1)^i*2*j*i)); }} [/asy]$

This post has been edited 1 time. Last edited by sonone, May 29, 2020, 8:10 PM

Asymptote

Fun

code

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4 Comments

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In your last example, why did you define dotfactor, since you never actually used a dot?

by G.G.Otto, May 29, 2020, 4:10 AM

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Just-in-case precaution

by sonone, May 29, 2020, 7:56 PM

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I think I've found the best asymptote grapher. It's called AutoGraph and was developed by PythonNut. See here. There are lots of different versions, the latest one that works on AoPS is V-5.

$[asy] /* AUTO-GRAPH V-5 alpha by PythonNut. Please do not plagerize, it's illegal :) Customizations: feel free to edit graph function */ real f(real x){ return 2x^3-9x^2+12x+1;} // type function to be graphed here /* x maximum and minimum */ int X_max = 10; int X_min = -10; /* y maximum and minimum */ int Y_max = 10; int Y_min = -10; /* toggle features */ bool mark_lattice = true; bool show_grid = false; bool mark_solutions = true; bool integral = false; bool maxima_and_minima = true; bool derivative = true; real[] Dpoints = {0.9,1.5,2.1,2.2,2.3}; /* other options */ int size = 500; real line_width = 0.75; pen color = heavygreen; pen opacity = opacity(0.9); real X_density = 1; real Y_density = 1; real ratio = 1; real res = 0.00005; pen fill = palegreen+linewidth(0.75)+opacity(0.8); pen aux = linewidth(0.75)+opacity(0.9); pen[] colors = {blue,red,green,pink,yellow,purple,orange}; real Dres = 0.00000001; /* The Code. Do not disturb unless you know what you are doing */ import math;import graph; size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);path s=(X_max,0)--(X_min,0); pen GRAPH = opacity+color+linewidth(line_width);real temp = X_min; while (! (f(temp) <= Y_max && f(temp) >= Y_min && temp < X_max)){temp += res;} if (integral){if (f(temp-res) > Y_max){ filldraw( (X_min,0)--(X_min,Y_max)--(temp,Y_max)--(temp,0)--cycle , fill,fill);}if (f(temp-res) < Y_min){ filldraw( (X_min,0)--(X_min,Y_min)--(temp,Y_min)--(temp,0)--cycle , fill,fill);}}real max = temp; while (f(max) <= Y_max && f(max) >= Y_min && max < X_max){max += res;}real min = temp; while (f(min) <= Y_max && f(min) >= Y_min && min > X_min){min -= res;} path graph = graph(f,min,max,n=2400);if (integral){ filldraw((min,0)--graph--(max,0)--cycle,fill,fill);}draw(graph,GRAPH,Arrows);temp = max+res; while (temp <= X_max){max=temp; while (! (f(temp) <= Y_max && f(temp) >= Y_min) && temp < X_max){ temp += res;}if (integral){if (f(temp-res) > Y_max){ filldraw( (max,0)--(max,Y_max)--(temp,Y_max)--(temp,0)--cycle , fill,fill);} if (f(temp-res) < Y_min){ filldraw( (max,0)--(max,Y_min)--(temp,Y_min)--(temp,0)--cycle , fill,fill); }}real max = temp; while (f(max) <= Y_max && f(max) >= Y_min && max < X_max){max += res;}real min = temp; while (f(min) <= Y_max && f(min) >= Y_min && min > X_min){ min -= res;}if (max <= X_max){path graph = graph(f,min,max,n=2400); if (integral){filldraw((min,0)--graph--(max,0)--cycle,fill,fill);}draw(graph,GRAPH,Arrows);} if (mark_solutions){dot(intersectionpoints(s,graph),green);}temp = max+res;continue;} if (integral){if (f(temp-res) > Y_max){ filldraw( (temp,0)--(temp,Y_max)--(X_max,Y_max)--(X_max,0)--cycle , fill,fill);} if (f(temp-res) < Y_min){ filldraw( (temp,0)--(temp,Y_min)--(X_max,Y_min)--(X_max,0)--cycle , fill,fill);}}temp = X_max; while (f(temp) <= Y_max && f(temp) >= Y_min && temp >= X_min){temp -= res;} if (f(X_max) <= Y_max && f(X_max) >= Y_min){ path graph2 = graph(f,temp,X_max,n=2400);if (integral){ filldraw( (temp,0)--graph2--(X_max,0)--cycle,fill,fill );}draw(graph2,GRAPH,Arrows); if (mark_solutions){dot(intersectionpoints(s,graph2),green);}} if (mark_lattice){for (real temp = X_min; temp <= X_max; ++temp){ if (f(temp)%1==0 && f(temp)<=Y_max && f(temp)>=Y_min){ dot((temp,f(temp)),color+linewidth(line_width*4));}}}if (maxima_and_minima){ real temp = X_min;real min = X_max;real max = X_min;while (temp <= X_max){ if (f(temp) >= max){max=f(temp);}if (f(temp) <= min){min=f(temp);}temp+=res;} if (max < X_max && max > X_min){draw((X_min,max)--(X_max,max),aux+blue);} if (min > X_min && min < X_max){draw((X_min,min)--(X_max,min),aux+blue);}} if (derivative){for (int i = 0; i < Dpoints.length; ++i){real Dpoint=Dpoints[i]; real h(real x){real temp = -(f(Dpoint)-f(Dpoint+Dres))/Dres*x; temp += (f(Dpoint)-f(Dpoint+Dres))/Dres*Dpoint;temp += f(Dpoint);return temp;} dot((Dpoint,f(Dpoint)),linewidth(3)+colors[i%colors.length]); draw(graph(h,X_min-0.2,X_max+0.2),aux+colors[i%colors.length]); draw((Dpoint,f(Dpoint))--(Dpoint,0),darkgrey+dashed);}} clip((X_min-0.2,Y_min-0.2)--(X_min-0.2,Y_max+0.2)--(X_max+0.2,Y_max+0.2)--(X_max+0.2,Y_min-0.2)--cycle); dot((0,0));picture main;xaxis("$x$",X_min,X_max,Ticks(l,X_density,(X_density/2),NoZero),Arrows); yaxis("$y$",Y_min,Y_max,Ticks(l,Y_density,(Y_density/2),NoZero),Arrows); if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));} add(main);/* Property of "PythonNut" 2011*/ [/asy]$

Now all your writing problems will be a lot easier! It's also very customizable and has a ton of features, look at the code!

$[asy] /* AUTO-GRAPH V-5 alpha by PythonNut. Please do not plagerize, it's illegal :) Customizations: feel free to edit graph function */ real f(real x){ return sin(x)-9x^2+12x+1;} // type function to be graphed here /* x maximum and minimum */ int X_max = 10; int X_min = -10; /* y maximum and minimum */ int Y_max = 10; int Y_min = -10; /* toggle features */ bool mark_lattice = true; bool show_grid = false; bool mark_solutions = true; bool integral = true; bool maxima_and_minima = true; bool derivative = true; real[] Dpoints = {0.9,1.5}; /* other options */ int size = 500; real line_width = 0.95; pen color = heavygreen; pen opacity = opacity(0.9); real X_density = 2; real Y_density = 2; real ratio = 1; real res = 0.00005; pen fill = palegreen+linewidth(0.75)+opacity(0.8); pen aux = linewidth(0.75)+opacity(0.9); pen[] colors = {blue,red,green,pink,yellow,purple,orange}; real Dres = 0.00000001; /* The Code. Do not disturb unless you know what you are doing */ import math;import graph; size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);path s=(X_max,0)--(X_min,0); pen GRAPH = opacity+color+linewidth(line_width);real temp = X_min; while (! (f(temp) <= Y_max && f(temp) >= Y_min && temp < X_max)){temp += res;} if (integral){if (f(temp-res) > Y_max){ filldraw( (X_min,0)--(X_min,Y_max)--(temp,Y_max)--(temp,0)--cycle , fill,fill);}if (f(temp-res) < Y_min){ filldraw( (X_min,0)--(X_min,Y_min)--(temp,Y_min)--(temp,0)--cycle , fill,fill);}}real max = temp; while (f(max) <= Y_max && f(max) >= Y_min && max < X_max){max += res;}real min = temp; while (f(min) <= Y_max && f(min) >= Y_min && min > X_min){min -= res;} path graph = graph(f,min,max,n=2400);if (integral){ filldraw((min,0)--graph--(max,0)--cycle,fill,fill);}draw(graph,GRAPH,Arrows);temp = max+res; while (temp <= X_max){max=temp; while (! (f(temp) <= Y_max && f(temp) >= Y_min) && temp < X_max){ temp += res;}if (integral){if (f(temp-res) > Y_max){ filldraw( (max,0)--(max,Y_max)--(temp,Y_max)--(temp,0)--cycle , fill,fill);} if (f(temp-res) < Y_min){ filldraw( (max,0)--(max,Y_min)--(temp,Y_min)--(temp,0)--cycle , fill,fill); }}real max = temp; while (f(max) <= Y_max && f(max) >= Y_min && max < X_max){max += res;}real min = temp; while (f(min) <= Y_max && f(min) >= Y_min && min > X_min){ min -= res;}if (max <= X_max){path graph = graph(f,min,max,n=2400); if (integral){filldraw((min,0)--graph--(max,0)--cycle,fill,fill);}draw(graph,GRAPH,Arrows);} if (mark_solutions){dot(intersectionpoints(s,graph),green);}temp = max+res;continue;} if (integral){if (f(temp-res) > Y_max){ filldraw( (temp,0)--(temp,Y_max)--(X_max,Y_max)--(X_max,0)--cycle , fill,fill);} if (f(temp-res) < Y_min){ filldraw( (temp,0)--(temp,Y_min)--(X_max,Y_min)--(X_max,0)--cycle , fill,fill);}}temp = X_max; while (f(temp) <= Y_max && f(temp) >= Y_min && temp >= X_min){temp -= res;} if (f(X_max) <= Y_max && f(X_max) >= Y_min){ path graph2 = graph(f,temp,X_max,n=2400);if (integral){ filldraw( (temp,0)--graph2--(X_max,0)--cycle,fill,fill );}draw(graph2,GRAPH,Arrows); if (mark_solutions){dot(intersectionpoints(s,graph2),green);}} if (mark_lattice){for (real temp = X_min; temp <= X_max; ++temp){ if (f(temp)%1==0 && f(temp)<=Y_max && f(temp)>=Y_min){ dot((temp,f(temp)),color+linewidth(line_width*4));}}}if (maxima_and_minima){ real temp = X_min;real min = X_max;real max = X_min;while (temp <= X_max){ if (f(temp) >= max){max=f(temp);}if (f(temp) <= min){min=f(temp);}temp+=res;} if (max < X_max && max > X_min){draw((X_min,max)--(X_max,max),aux+blue);} if (min > X_min && min < X_max){draw((X_min,min)--(X_max,min),aux+blue);}} if (derivative){for (int i = 0; i < Dpoints.length; ++i){real Dpoint=Dpoints[i]; real h(real x){real temp = -(f(Dpoint)-f(Dpoint+Dres))/Dres*x; temp += (f(Dpoint)-f(Dpoint+Dres))/Dres*Dpoint;temp += f(Dpoint);return temp;} dot((Dpoint,f(Dpoint)),linewidth(3)+colors[i%colors.length]); draw(graph(h,X_min-0.2,X_max+0.2),aux+colors[i%colors.length]); draw((Dpoint,f(Dpoint))--(Dpoint,0),darkgrey+dashed);}} clip((X_min-0.2,Y_min-0.2)--(X_min-0.2,Y_max+0.2)--(X_max+0.2,Y_max+0.2)--(X_max+0.2,Y_min-0.2)--cycle); dot((0,0));picture main;xaxis("$x$",X_min,X_max,Ticks(l,X_density,(X_density/2),NoZero),Arrows); yaxis("$y$",Y_min,Y_max,Ticks(l,Y_density,(Y_density/2),NoZero),Arrows); if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));} add(main);/* Property of "PythonNut" 2011*/ [/asy]$

-piphi

by piphi, Jun 3, 2020, 2:22 AM

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Thats really cool! Even though writing problem diagrams aren't that hard, I see what you mean!

by sonone, Jun 3, 2020, 7:36 PM

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I still exist as well.
by G.G.Otto, Aug 11, 2023, 2:44 AM
hello I'm still here lol
by player01, Aug 6, 2022, 6:24 PM
[REVIVAL] I will start posting more calculator relating posts very soon. Even though school has been busy, I have been programming my calculators a decent amount, so I have a lot to share...
by sonone, Feb 18, 2022, 10:29 PM
wow its been like 2.5 years since geo class
by pieMax2713, Feb 4, 2022, 8:38 PM
@violin21, I've been very busy with school lately and haven't been able to add another lesson. I will when i get a free moment
by sonone, Aug 19, 2021, 12:45 AM
ORZ CODER
by samrocksnature, Aug 9, 2021, 9:57 PM
Could you make more Asymptote lessons on your "How to do Asymptote" blog?
by violin21, Aug 9, 2021, 7:26 PM
You can take it, just C&P the CSS into your CSS area
by sonone, Apr 17, 2021, 10:08 PM
how can we take the CSS if we have permission to not take it?
by GoogleNebula, Apr 17, 2021, 5:22 PM
That is awesome!
by sonone, Apr 15, 2021, 10:09 PM
I modified your dodecahedron and got:
[asy]
import three;
import solids;
size(300);
currentprojection=orthographic(0,1.3,1.2);
light(0,5,10);

real phi=(sqrt(6)+1)/3;
real g=(phi-1)/2;
real s=1/2;
real a=sqrt(1-phi*phi/4-g*g)+phi/2;

triple[] d;
d[0]=(phi
by Andrew2019, Mar 26, 2021, 12:15 AM
Not too many, just changing the color here and there. I really like your CSS!
by sonone, Feb 2, 2021, 10:35 AM
Nice!

I see you're making changes to the CSS.
by G.G.Otto, Feb 1, 2021, 9:26 PM
I'm learning Java now!
by sonone, Feb 1, 2021, 5:56 PM
And I took part of it from CaptainFlint and then added a ton of modifications.
by G.G.Otto, Dec 1, 2020, 8:56 AM
fixed $\text{[math]}$
by sonone, Apr 25, 2020, 8:43 PM
Change in progress...
by sonone, Apr 25, 2020, 8:42 PM
When it says "At least 11 users clicked that button" it's incorrect since one person could have just posted 11 times. It should say "At most 11 users click that button".
by G.G.Otto, Apr 25, 2020, 8:26 PM
see this PM
by sonone, Apr 25, 2020, 7:03 PM
I can't get the cursor to work.
by G.G.Otto, Apr 25, 2020, 6:38 PM
If the cursor is confusing, where you are actually pointing in a front of the ship
by sonone, Apr 25, 2020, 11:04 AM
It's ok $\text{[math]}$
by sonone, Apr 23, 2020, 5:30 PM
Sorry I haven't been posting. I've got a Research Paper (for Roman History) due in a week.
by G.G.Otto, Apr 22, 2020, 11:15 PM
You should download it, as it's really useful when learning python. You can find out more here
by G.G.Otto, Apr 19, 2020, 10:04 PM
No. I don't have IDLE.
by sonone, Apr 18, 2020, 7:49 PM
Do you have IDLE installed on your computer? If so, I can give you a couple really cool codes that made that don't work in the AoPS widgets.
by G.G.Otto, Apr 14, 2020, 6:47 AM
I don't know how to change it....
by G.G.Otto, Apr 5, 2020, 5:58 PM
Do you know how the change the into thing above my avatar a different color? It's too hard to see.
by sonone, Apr 5, 2020, 2:08 PM
WELCOME TO MY BLOG!
by sonone, Mar 31, 2020, 4:56 PM

98 shouts

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Scratch art

by sonone, May 28, 2020, 7:16 PM

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