kivy_mandlebrot.py

"""
A simple Mandlebrot explorer in Kivy! Drag mouse to translate, multitouch-zoom to zoom, and scroll to increase/decrease number of iterations.
"""
from kivy.app import App
from kivy.core.window import Window
from kivy.uix.effectwidget import AdvancedEffectBase
from kivy.lang import Builder
from kivy.vector import Vector

SHADER = """
uniform vec2 position;
uniform float zoom;
uniform int iterations;
uniform vec3 palette[16];
const vec2 bottom_left = vec2(-2.0, -1.5);
vec2 pos;
float zx, zy, oldzx;
int n;

vec4 effect(vec4 color, sampler2D texture, vec2 tex_coords, vec2 coords){
  pos = (3.0 * tex_coords + bottom_left) / zoom - position + .5;
  zx = position.x - .5;
  zy = position.y - .5;

  for(n = 0; n < iterations; n++){
    if(zx * zx + zy * zy > 4.0) break;
  	oldzx = zx;
	zx = zx * zx - zy * zy + pos.x;
    zy = 2.0 * oldzx * zy + pos.y;}

  if(n < iterations) return vec4(palette[int(mod(float(n), 16.0))], 1.0);
  else return vec4(0.0, 0.0, 0.0, 1.0);}
"""

PALETTE = [[0.259, 0.118, 0.059], [0.098, 0.027, 0.102], [0.035, 0.004, 0.184], [0.016, 0.016, 0.286],
           [0.0  , 0.027, 0.392], [0.047, 0.173, 0.541], [0.094, 0.322, 0.694], [0.224, 0.49 , 0.82 ],
           [0.525, 0.71 , 0.898], [0.827, 0.925, 0.973], [0.945, 0.914, 0.749], [0.973, 0.788, 0.373],
           [1.0  , 0.667, 0.0  ], [0.8  , 0.502, 0.0  ], [0.6  , 0.341, 0.0  ], [0.416, 0.204, 0.012]]

EFFECT = AdvancedEffectBase()
EFFECT.glsl = SHADER
EFFECT.uniforms = {'position': (.5, .5), 'zoom': 1.0, 'iterations': 30, 'palette': PALETTE}

KV = """
#:import EFFECT __main__.EFFECT
EffectWidget:
    effects: EFFECT,
"""
ZOOM = 500 # multitouch zooming speed (inversely proportional)
TRANSLATE = 3 # multitouch translation speed

class Mandlebrot(App):
    def build(self):
        self._touches = []
        Window.bind(on_touch_up=self._on_touch_up,
                    on_touch_down=self._on_touch_down,
                    on_touch_move=self._on_touch_move)
        return Builder.load_string(KV)

    def transform_on_touch(self, touch):
        anchor = Vector(self._touches[-2].pos)
        current = Vector(touch.pos) - anchor
        previous = Vector(touch.ppos) - anchor
        travel_distance = (current.length() - previous.length()) / ZOOM
        zoom = EFFECT.uniforms['zoom']
        EFFECT.uniforms['zoom'] = max(.000001, zoom * (1 + travel_distance))

    def _on_touch_up(self, _, touch):
        self._touches.remove(touch)

    def _on_touch_down(self, _, touch):
        if touch.is_mouse_scrolling:
            iterations = EFFECT.uniforms['iterations']
            iterations += (-1)**(touch.button == 'scrollup')
            EFFECT.uniforms['iterations'] = max(1, iterations)
        self._touches.append(touch)

    def _on_touch_move(self, _, touch):
        if touch.button == 'left':
            if len(self._touches) == 1:
                x, y = EFFECT.uniforms['position']
                zoom = EFFECT.uniforms['zoom']
                x += touch.dsx * TRANSLATE / zoom
                y += touch.dsy * TRANSLATE / zoom
                EFFECT.uniforms['position'] = x, y
            else:
                self.transform_on_touch(touch)

if __name__ == '__main__':
    Mandlebrot().run()