Logistic Map.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 逻辑斯谛映射\n",
    "非线性混沌的一种，\n",
    "基于逻辑斯谛方程\n",
    "$$\n",
    "x_{t+1} = rx_t(1-x_t),  x_0 \\in [0,1],  r \\in [0,4]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%matplotlib notebook\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Chaos:\n",
    "    \n",
    "    def __init__(self, x0, r):\n",
    "        self.x = x0;\n",
    "        self.r = r;\n",
    "        \n",
    "    def update(self):\n",
    "        self.x = self.r * (1-self.x) * self.x;\n",
    "        \n",
    "    def generate_sequence(self ,length):\n",
    "        sequence = []\n",
    "        for i in range(length):\n",
    "            sequence.append(self.x);\n",
    "            self.update();\n",
    "            \n",
    "        return sequence;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.6,\n",
       " 0.7200000000000001,\n",
       " 0.6047999999999999,\n",
       " 0.7170508800000002,\n",
       " 0.6086667464736766]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chao1 = Chaos(0.6, 3);\n",
    "se = chao1.generate_sequence(5);\n",
    "se"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
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       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
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       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
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       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
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       "            if (buttonGroup.hasChildNodes()) {\n",
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       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
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       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
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       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "<img 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\" width=\"432\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots();\n",
    "se = Chaos(0.1, 4);\n",
    "r = 2.5;\n",
    "\n",
    "while r < 4:\n",
    "    se.r = r;\n",
    "    tails = se.generate_sequence(1000)[950:];\n",
    "    #markersize\n",
    "    ax.plot([r] * len(tails), tails, 'b.', ms = 0.6);\n",
    "    r += 0.05\n",
    "    \n",
    "ax.set_xlabel('$r$', fontsize = 14);\n",
    "ax.set_ylabel('$x_t$', fontsize = 14);\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}