Mathematica, 413409 bytes
{n,p}=Input[];Clear@f;_~f~_=0;0~f~0=1;r=RandomInteger;For[i=0=Input[];m=999;Clear@f;_~f~_=0;0~f~0=1;r=RandomInteger;For[i=0,i<999i<m,++i,For[x=999;y=0For[x=m;y=0,f[x+1,y]+f[x-1,y]+f[x,y+1]+f[x,y-1]<1,a=b=-999;While[x+a<0||y+b<0||m;While[x+a<0||y+b<0||(y+b)/(x+a)>Tan[Pi/6],a=-r@1;b=r@2-1];x+=a;y+=b];x~f~y=1];Graphics[{White,g=Point/@Join@@{c=Cases[Join@@Table[{i,j}-1,{i,100m},{j,100m}],{i_,j_}/;i~f~j>0],c.{{1,0},{0,-1}}},Array[Rotate[g,Pi#/3,{0,0}]&,6]},Background->Black,ImageSize->n*p,ImageMargins->n(1-p)/2]
{n,p}=Input[];
m = 999;
ClearAll@f;
_~f~_ = 0;
0~f~0 = 1;
r = RandomInteger;
For[i = 0, i < 999m, ++i,
For[x = 999;m; y = 0,
f[x + 1, y] + f[x - 1, y] + f[x, y + 1] + f[x, y - 1] < 1,
a = b = -999;m;
While[x + a < 0 || y + b < 0 || (y + b)/(x + a) > Tan[Pi/6],
a = -r@1;
b = r@2 - 1
];
x += a;
y += b
];
x~f~y = 1
];
Graphics[
{White, g =
Point /@
Join @@ {c =
Cases[Join @@ Table[{i, j} - 1, {i, 100m}, {j, 100m}], {i_, j_} /;
i~f~j > 0], c.{{1, 0}, {0, -1}}},
Array[Rotate[g, Pi #/3, {0, 0}] &, 6]},
Background -> Black,
ImageSize -> n*p,
ImageMargins -> n (1 - p)/2
]
It takes something like half a minute to generate a snowflake with the given parameters. You can speed it up by replacingchanging the value of m from 999s with to 99s, but then the result looks a bit sparse. Likewise, you can crank up the quality by using larger numbers, but then it'll take agesvery long.
Mathematica, 413 bytes
{n,p}=Input[];Clear@f;_~f~_=0;0~f~0=1;r=RandomInteger;For[i=0,i<999,++i,For[x=999;y=0,f[x+1,y]+f[x-1,y]+f[x,y+1]+f[x,y-1]<1,a=b=-999;While[x+a<0||y+b<0||(y+b)/(x+a)>Tan[Pi/6],a=-r@1;b=r@2-1];x+=a;y+=b];x~f~y=1];Graphics[{White,g=Point/@Join@@{c=Cases[Join@@Table[{i,j}-1,{i,100},{j,100}],{i_,j_}/;i~f~j>0],c.{{1,0},{0,-1}}},Array[Rotate[g,Pi#/3,{0,0}]&,6]},Background->Black,ImageSize->n*p,ImageMargins->n(1-p)/2]
{n,p}=Input[];
ClearAll@f;
_~f~_ = 0;
0~f~0 = 1;
r = RandomInteger;
For[i = 0, i < 999, ++i,
For[x = 999; y = 0,
f[x + 1, y] + f[x - 1, y] + f[x, y + 1] + f[x, y - 1] < 1,
a = b = -999;
While[x + a < 0 || y + b < 0 || (y + b)/(x + a) > Tan[Pi/6],
a = -r@1;
b = r@2 - 1
];
x += a;
y += b
];
x~f~y = 1
];
Graphics[
{White, g =
Point /@
Join @@ {c =
Cases[Join @@ Table[{i, j} - 1, {i, 100}, {j, 100}], {i_, j_} /;
i~f~j > 0], c.{{1, 0}, {0, -1}}},
Array[Rotate[g, Pi #/3, {0, 0}] &, 6]},
Background -> Black,
ImageSize -> n*p,
ImageMargins -> n (1 - p)/2
]
It takes something like a minute to generate a snowflake with the given parameters. You can speed it up by replacing the 999s with 99s, but then the result looks a bit sparse. Likewise, you can crank up the quality by using larger numbers, but then it'll take ages.
Mathematica, 409 bytes
{n,p}=Input[];m=999;Clear@f;_~f~_=0;0~f~0=1;r=RandomInteger;For[i=0,i<m,++i,For[x=m;y=0,f[x+1,y]+f[x-1,y]+f[x,y+1]+f[x,y-1]<1,a=b=-m;While[x+a<0||y+b<0||(y+b)/(x+a)>Tan[Pi/6],a=-r@1;b=r@2-1];x+=a;y+=b];x~f~y=1];Graphics[{White,g=Point/@Join@@{c=Cases[Join@@Table[{i,j}-1,{i,m},{j,m}],{i_,j_}/;i~f~j>0],c.{{1,0},{0,-1}}},Array[Rotate[g,Pi#/3,{0,0}]&,6]},Background->Black,ImageSize->n*p,ImageMargins->n(1-p)/2]
{n,p}=Input[];
m = 999;
ClearAll@f;
_~f~_ = 0;
0~f~0 = 1;
r = RandomInteger;
For[i = 0, i < m, ++i,
For[x = m; y = 0,
f[x + 1, y] + f[x - 1, y] + f[x, y + 1] + f[x, y - 1] < 1,
a = b = -m;
While[x + a < 0 || y + b < 0 || (y + b)/(x + a) > Tan[Pi/6],
a = -r@1;
b = r@2 - 1
];
x += a;
y += b
];
x~f~y = 1
];
Graphics[
{White, g =
Point /@
Join @@ {c =
Cases[Join @@ Table[{i, j} - 1, {i, m}, {j, m}], {i_, j_} /;
i~f~j > 0], c.{{1, 0}, {0, -1}}},
Array[Rotate[g, Pi #/3, {0, 0}] &, 6]},
Background -> Black,
ImageSize -> n*p,
ImageMargins -> n (1 - p)/2
]
It takes something like half a minute to generate a snowflake with the given parameters. You can speed it up by changing the value of m from 999 to 99, but then the result looks a bit sparse. Likewise, you can crank up the quality by using larger numbers, but then it'll take very long.
And here are two animations of the Brownian tree growing (10 particles per wedge per frame):
And here are two animations of the Brownian tree growing (10 particles per wedge per frame):