Examples.ipynb

Kernel: Python 3 (system-wide)

Iterated Function System Fractal Generator -- Examples

from IFSFGL import *

The Barnsely Fern

BW = np.array([0.01,.85,0.07,.07])

B1 = np.array([[0,0,0.5],[0, 0.16, 0],[0,0,1]]) # Translate(.5,0) @ ScaleXY(0,.16)
B2 = np.array([[0.849,0.037,0.075],[-0.037, 0.849, 0.183],[0,0,1]]) # about                   Translate(0.075,0.183) @ Rotate(-0.037) @ Scale(0.849)
B3 = np.array([[0.197, -0.226, 0.4],[0.226, 0.197, 0.049],[0,0,1]])
B4 = np.array([[-0.15,0.283,0.575],[0.26, 0.237, -0.084],[0,0,1]])

BT = [B1, B2, B3, B4]

plot_figures(generate_figures(1,[XBox],BT), size=5)

fern = Fractal(BT, weights=BW, size=20)

fern.add_points(100_000)

fern.display_pic()

G = generate_points(100_000, BT, BW)

Generating 100000 points... Finished in 2.1689255237579346 seconds.

fern.load_in_points(G)

fern.display_pic()

fern.developement

200000

The Crab

C1 = Translate(0.5,0.15) @ Rotate(np.pi/4) @ Scale(1/4)
C2 = Scale(1/2)
C3 = Translate(-.5,0.15) @ Rotate(-np.pi/4) @ Scale(1/4)
C4 = Rotate(-np.pi/6) @ Scale(1/2)
C5 = Rotate(np.pi/6) @ Scale(1/2)

CT = [C1, C2, C3, C4, C5]

crab = Fractal(CT)

crab.add_points(1_000_000)

crab.pic

Keir's Leaf

LW = np.array([0.64,0.12,0.12,0.12])

L1 = Translate(0.15,0.3) @ Scale(0.7)
L2 = Translate(0.35,0) @ Rotate(np.pi/4) @ Scale(0.35*np.sqrt(2))
L3 = Translate(0.3,0.35) @ Rotate(-np.pi/4) @ Scale(0.35*np.sqrt(2))
L4 = Translate(0.45,0.2) @ ScaleXY(1/10,3/10)

LT = [L1, L2, L3, L4]

leaf = Fractal(LT, LW, size = 15)
leaf.add_points(1_000_000)

leaf.pic

Kotch Curve

k1 = Scale(1/3)
k2 = Translate(1,0) @ Rotate(np.pi/3) @ Scale(1/3)
k3 = Translate(1.5,np.sin(np.pi/3)) @ Rotate((-1*np.pi)/3) @ Scale(1/3)
k4 = Translate(2,0) @ Scale(1/3)

kT = [k1,k2,k3,k4]

kotchCurve = Fractal(kT, size=20)
# kotchCurve.add_points(1_000_000)
# kotchCurve.pic

kotchCurve.make_gif(name='point3', n=1_000_000, zoom=3.1, frames=30, zoomPoint=(1.5,np.sin(np.pi/3)))

Alyson's Alteration

a1 = Scale(1/3)
a2 = Translate(1.5,-np.sin(np.pi/3)) @ Rotate(2*np.pi/3) @ Scale(1/3)
a3 = Translate(2,0) @ Rotate(-2*np.pi/3) @ Scale(1/3)
a4 = Translate(2,0) @ Scale(1/3)

aT = [a1,a2,a3,a4]

plot_figures(generate_figures(1,[np.array([[0,0,1],[3,0,1]]).T],aT))

alysonsAlt = Fractal(aT, size = 10)

alysonsAlt.add_points(1_000_000)

alysonsAlt.pic

Kotch Snowflake

s=np.sin(pi/3)
c=np.cos(pi/3)

Line1 = np.array([ [0,1.5], [3*s,0], [1,1]])
Line2 = np.array([ [-1.5,0], [0,3*s], [1,1]])
Line3 = np.array([ [1.5,-1.5], [0,0], [1,1]])

L11 = Translate(0,2*s) @ Scale(1/3)
L12 = Translate(.5+s**2,2*s-c*s) @ Rotate((pi/3)) @ Scale(1/3)
L13 = Translate(1.5-s**2,2*s-c*s) @ Rotate((-1*pi)/3) @ Scale(1/3)
L14 = Translate(1,0) @ Scale(1/3)
T1_L = [L11,L12,L13,L14]

L21 = Translate(0,2*s) @ Scale(1/3)
L22 = Translate(-s**2,2*s-c*s) @ Rotate(pi/3) @ Scale(1/3)
L23 = Translate(-2+s**2,2*s-c*s) @ Rotate((-1*pi)/3) @ Scale(1/3)
L24 = Translate(-1,0) @ Scale(1/3)
T2_L = [L21,L22,L23,L24]

L31 = Translate(-1,0) @ Scale(1/3)
L32 = Translate(-c/2,-s/2) @ Rotate(-pi/3) @ Scale(1/3)
L33 = Translate(c/2,-s/2) @ Rotate(pi/3) @ Scale(1/3)
L34 = Translate(1,0) @ Scale(1/3)
T3_L = [L31,L32,L33,L34]


plot_figures(generate_figures(4, [Line1], T1_L) + generate_figures(4, [Line2], T2_L)+ generate_figures(4, [Line3], T3_L))

Koch Tessalation

T = T1_L + T2_L + T3_L

tessellation = Fractal(T)

tessellation.add_points(1_000_000)

tessellation.pic

Name

name = Fractal(word_fractal('name'), size=10)
name.add_points(100000)
name.display_pic()

$\pi$-inspired Fractals

line = np.array([[0, 0, 1], [1, 0, 1]], dtype = np.float64).T

P1 = Translate(-1/5**(1/pi),0) @ Scale(1/5**(1/pi))
P2 = Scale(1/5**(1/pi))
P3 = Translate(1/5**(1/pi),0) @ Scale(1/5**(1/pi))
P4 = Rotate(-pi/2) @ Scale(1/5**(1/pi))
P5 = Translate(1/5**(1/pi),0) @ Rotate(-pi/2.5) @ Scale(1/5**(1/pi))

P = [P1,P2,P3,P4,P5]

plot_figures([line] + generate_figures(1,[line],P))

pFractal = Fractal(P)

pFractal.add_points(5_000_000)

pFractal.pic

pFractal.dimension(n=10_000_000, endSize=15)

Serpinski Triangle

E1 = Scale(1/2)
E2 = Translate(1/2,0) @ Scale(1/2)
E3 = Translate(cos(pi/3)/2, sin(pi/3)/2) @ Scale(1/2)

E = [E1, E2, E3]

serpinski = Fractal(E)
serpinski.add_points(1_000_000)
serpinski.pic

serpinski.dimension()

Squiggle

S1 = Scale(1/4)
S2 = Translate(1/4,0) @ Rotate(pi/2) @ Scale(1/4)
S3 = Translate(1/4,1/4) @ Scale(1/4)
S4 = Translate(1/2,1/4) @ Rotate(-pi/2) @ Scale(1/4)
S5 = Translate(1/2,0) @ Rotate(-pi/2) @ Scale(1/4)
S6 = Translate(1/2,-1/4) @ Scale(1/4)
S7 = Translate(3/4,-1/4) @ Rotate(pi/2) @ Scale(1/4)
S8 = Translate(3/4,0) @ Scale(1/4)

S = [S1,S2,S3,S4,S5,S6,S7,S8]

squiggle = Fractal(S)
squiggle.add_points(1_000_000)
squiggle.pic

Dragon Curve

D1 = Rotate(-pi/4) @ Scale(cos(pi/4))
D2 = Translate(1, 0) @ Rotate(-3*pi/4) @ Scale(cos(pi/4))

D = [D1, D2]

plot_figures([line] + generate_figures(1,[line],D))

dragon = Fractal(D)

dragon.add_points(1_000_000)

dragon.pic

Dill

from random import *

ReflectY = np.array([[-1, 0, 0],
                     [0, 1, 0],
                     [0, 0, 1]])

stem = [Translate(.5,0) @ Rotate(-.4) @ ScaleXY(0,.16),
        Translate(0.236,0.132) @ Rotate(.037) @ Scale(0.65)]

h = 0.645
k = 0.41

w = .3

neg = -1
pos = 1

while (neg != pos) and (abs(neg-pos) != 1):
    neg = 0
    pos = 0
    parts = []
    for _ in range(1):
        x = random() * (2 * w) - w
        y = - .25 * (x - w) * (x + w) + .18
        r = sqrt(y**2 + x**2)
        if x >= 0:
            parts += [Translate(h,k) @ Rotate(-arctan(x/y)) @ Scale(r) @ Translate(-.5,0)]
            pos += 1
        else:
            parts += [Translate(h,k) @ ReflectY @ Rotate(-arctan(abs(x)/y)) @ Scale(r) @ Translate(-.5,0)]
            neg += 1

dillWeights = np.zeros(2 + len(parts))
dillWeights[0:2] = .4
dillWeights[2:] = .2 / len(parts)
Dill = stem + parts

figs = generate_figures(2,[XBox],Dill)
plot_figures(figs, size=5)

dillFractal = Fractal(Dill, weights=dillWeights, size=25)

dillFractal.add_points(1_000_000)

dillFractal.pic