2022-12-02_caustique.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.002832Z",
     "iopub.status.busy": "2022-09-16T06:50:17.002540Z",
     "iopub.status.idle": "2022-09-16T06:50:17.009923Z",
     "shell.execute_reply": "2022-09-16T06:50:17.009225Z"
    }
   },
   "outputs": [],
   "source": [
    "figpath = '2022-12-02_caustique'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
     "iopub.status.idle": "2022-09-16T06:50:17.665184Z",
     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 4 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.673182Z",
     "iopub.status.busy": "2022-09-16T06:50:17.672981Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.674999Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 10 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.677775Z",
     "iopub.status.busy": "2022-09-16T06:50:17.677563Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.685757Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import datetime\n",
    "import numpy as np\n",
    "\n",
    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
    "from dataclasses import dataclass, asdict, field\n",
    "\n",
    "@dataclass\n",
    "class init:\n",
    "    figpath: str = figpath # Folder to store images\n",
    "    fig_width: float = 12 # width of figure\n",
    "    phi: float = 1.61803 # beauty is gold\n",
    "    N_PG_show: float = 5 # number of PG to show in plot_PG\n",
    "    tag: str = 'caustique' # Tag\n",
    "    ext: str = 'png' # Extension for output\n",
    "    nx: int = 5*2**PRECISION # number of pixels (vertical)\n",
    "    ny: int = 5*2**PRECISION # number of pixels (horizontal)\n",
    "    nframe: int = 1 # number of frames\n",
    "    bin_dens: int = 4 # relative bin density\n",
    "    bin_spectrum: int = 3 # bin spacing in spectrum\n",
    "    seed: int = 8601 # seed for RNG\n",
    "    H: float = 1.5 # depth of the pool\n",
    "    variation: float = .4 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation\n",
    "    scale: float = 200 # sf\n",
    "    B_sf: float = 0.25 # bandwidth in sf\n",
    "    V_Y: float = 0.3 # horizontal speed\n",
    "    V_X: float = 0.3 # vertical speed\n",
    "    B_V: float = 1.0 # bandwidth in speed\n",
    "    theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
    "    B_theta: float = 2*np.pi/3 # bandwidth in theta\n",
    "    min_lum: float = .2 # diffusion level for the rendering\n",
    "    gamma: float = 2.8 # Gamma exponant to convert luminosity to luminance\n",
    "    fps: float = 18 # frames per second\n",
    "    multispectral: bool = True # Compute caustics on the full spectrogram.\n",
    "    cache: bool = True # Cache intermediate output.\n",
    "    verbose: bool = False # Displays more verbose output.\n",
    "    do_display: bool = False # Displays images in notebook.\n",
    "    do_recompute: bool = False # Restart each computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
     "iopub.status.busy": "2022-09-16T06:50:17.688504Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving our simulations in=2022-12-02_caustique\n"
     ]
    }
   ],
   "source": [
    "print(f'Saving our simulations in={figpath}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.722173Z",
     "iopub.status.busy": "2022-09-16T06:50:17.721924Z",
     "iopub.status.idle": "2022-09-16T06:50:17.725840Z",
     "shell.execute_reply": "2022-09-16T06:50:17.725292Z"
    }
   },
   "outputs": [],
   "source": [
    "opt = init()\n",
    "opt.figpath = figpath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "init(figpath='2022-12-02_caustique', fig_width=12, phi=1.61803, N_PG_show=5, tag='caustique', ext='png', nx=5120, ny=5120, nframe=1, bin_dens=4, bin_spectrum=3, seed=8601, H=1.5, variation=0.4, scale=200, B_sf=0.25, V_Y=0.3, V_X=0.3, B_V=1.0, theta=2.399988291783386, B_theta=2.0943951023931953, min_lum=0.2, gamma=2.8, fps=18, multispectral=True, cache=True, verbose=False, do_display=False, do_recompute=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "if opt.nframe==1: opt.ext = 'png'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
     "iopub.status.idle": "2022-09-16T06:50:17.741165Z",
     "shell.execute_reply": "2022-09-16T06:50:17.740716Z"
    }
   },
   "outputs": [],
   "source": [
    "def make_gif(gifname, fnames, fps, do_delete=True):\n",
    "    import imageio\n",
    "\n",
    "    with imageio.get_writer(gifname, mode='I', fps=fps) as writer:\n",
    "        for fname in fnames:\n",
    "            writer.append_data(imageio.imread(fname))\n",
    "\n",
    "    from pygifsicle import optimize\n",
    "    optimize(str(gifname))\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return gifname\n",
    "\n",
    "# https://moviepy.readthedocs.io/en/latest/getting_started/videoclips.html#imagesequenceclip\n",
    "def make_mp4(mp4name, fnames, fps, do_delete=True):\n",
    "    import moviepy.editor as mpy\n",
    "    clip = mpy.ImageSequenceClip(fnames, fps=fps)\n",
    "    clip.write_videofile(mp4name, fps=fps, codec='libx264', verbose=False, logger=None)\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return mp4name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Utilities to compute the spectrum of the blue sky and convert them later to RGB values (check out https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for details)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
     "iopub.status.busy": "2022-09-16T06:50:17.743461Z",
     "iopub.status.idle": "2022-09-16T06:50:17.757701Z",
     "shell.execute_reply": "2022-09-16T06:50:17.757282Z"
    }
   },
   "outputs": [],
   "source": [
    "from lambda2color import Lambda2color, xyz_from_xy\n",
    "\n",
    "# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py\n",
    "def planck(wav, T):\n",
    "    import scipy.constants as const\n",
    "    c = const.c # c = 3.0e+8\n",
    "    h = const.h # h = 6.626e-34\n",
    "    k = const.k # k = 1.38e-23\n",
    "    a = 2.0*h*c**2\n",
    "    b = h*c/(wav*k*T)\n",
    "    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )\n",
    "    return intensity\n",
    "\n",
    "def scattering(wav, a=0.005, p=1.3, b=0.45):\n",
    "    \"\"\"\n",
    "    b is  proportionate  to  the  column  density  of  aerosols\n",
    "    along  the  path  of  sunlight,  from  outside  the  atmosphere\n",
    "    to  the  point  of  observation\n",
    "    \n",
    "    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details\n",
    "\n",
    "    \"\"\"\n",
    "    # converting wav in µm:\n",
    "    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen\n",
    "    intensity *= (wav/1e-6)**-4\n",
    "    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols\n",
    "    return intensity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## computing the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.760440Z",
     "iopub.status.busy": "2022-09-16T06:50:17.760224Z",
     "iopub.status.idle": "2022-09-16T06:50:17.823069Z",
     "shell.execute_reply": "2022-09-16T06:50:17.822569Z"
    }
   },
   "outputs": [],
   "source": [
    "import shutil\n",
    "import hashlib\n",
    "from tqdm import tqdm, trange\n",
    "import MotionClouds as mc\n",
    "class Caustique:\n",
    "    def __init__(self, opt):\n",
    "        \"\"\"\n",
    "        Image coordinates follow 'ij' indexing, that is,\n",
    "        * their origin at the top left,\n",
    "        * the X axis is vertical and goes \"down\",\n",
    "        * the Y axis is horizontal and goes \"right\".\n",
    "\n",
    "        \"\"\"\n",
    "        self.mc = mc\n",
    "        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)\n",
    "        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical\n",
    "        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal\n",
    "        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')\n",
    "        self.opt = opt\n",
    "        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary\n",
    "        self.d = vars(opt)\n",
    "        os.makedirs(self.opt.figpath, exist_ok=True)\n",
    "        self.cachepath = os.path.join('/tmp', self.opt.figpath)\n",
    "        if opt.verbose: print(f'{self.cachepath=}')\n",
    "        os.makedirs(self.cachepath, exist_ok=True)\n",
    "\n",
    "        # a standard white:\n",
    "        illuminant_D65 = xyz_from_xy(0.3127, 0.3291), \n",
    "        illuminant_sun = xyz_from_xy(0.325998, 0.335354)\n",
    "        # color conversion class\n",
    "        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),\n",
    "                               green=xyz_from_xy(0.30, 0.60),\n",
    "                               blue=xyz_from_xy(0.15, 0.06),\n",
    "                               white=illuminant_sun)\n",
    "        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9\n",
    "        self.N_wavelengths = len(self.wavelengths)\n",
    "        # multiply by the spectrum of the sky\n",
    "        intensity5800 = planck(self.wavelengths, 5800.)\n",
    "        scatter = scattering(self.wavelengths)\n",
    "        self.spectrum_sky = intensity5800 * scatter\n",
    "        self.spectrum_sky /= self.spectrum_sky.max()\n",
    "\n",
    "    def wave(self):\n",
    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
    "        if os.path.isfile(filename):\n",
    "            z = np.load(filename)\n",
    "        else:\n",
    "            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds\n",
    "            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)\n",
    "            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,\n",
    "                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,\n",
    "                                    theta=self.opt.theta, B_theta=self.opt.B_theta)\n",
    "            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))\n",
    "            if self.opt.cache: np.save(filename, z)\n",
    "        return z\n",
    "\n",
    "    def transform(self, z_, modulation=1.):\n",
    "        xv, yv = self.xv.copy(), self.yv.copy()\n",
    "\n",
    "        dzdx = z_ - np.roll(z_, 1, axis=0)\n",
    "        dzdy = z_ - np.roll(z_, 1, axis=1)\n",
    "        xv = xv + modulation * self.opt.H * dzdx\n",
    "        yv = yv + modulation * self.opt.H * dzdy\n",
    "\n",
    "        xv = np.mod(xv, 1)\n",
    "        yv = np.mod(yv, self.ratio)\n",
    "\n",
    "        return xv, yv\n",
    "\n",
    "    def plot(self, z, image=None, do_color=True, dpi=50):\n",
    "\n",
    "        # output filename        \n",
    "        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging\n",
    "        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'\n",
    "        if os.path.isfile(output_filename) and not(self.opt.do_recompute):\n",
    "            return output_filename\n",
    "        else:\n",
    "            # 1/ do the raytracing of image through z:\n",
    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            # a fixed image in degree of contrast (from 0=black to 1=white)\n",
    "            if image is None: image = np.ones((self.opt.nx, self.opt.ny))\n",
    "\n",
    "            #hist = self.do_raytracing(z)\n",
    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\n",
    "\n",
    "            if self.opt.multispectral:\n",
    "\n",
    "                #image_rgb = self.cs_srgb.spec_to_rgb(hist)\n",
    "                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))\n",
    "                for i_frame in tqdm(range(self.opt.nframe)):\n",
    "                    for ii_wavelength, i_wavelength in enumerate(range(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum)):\n",
    "                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths\n",
    "                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
    "                        hist_, edge_x, edge_y = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                               bins=[binsx, binsy],\n",
    "                                                               weights=image.ravel(),\n",
    "                                                               range=[[0, 1], [0, self.ratio]],\n",
    "                                                               density=True)\n",
    "\n",
    "                        spec = np.zeros((self.N_wavelengths))\n",
    "                        spec[i_wavelength] = 1\n",
    "                        rgb = self.cs_srgb.spec_to_rgb(spec)\n",
    "                        rgb *= self.spectrum_sky[i_wavelength]\n",
    "                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]\n",
    "\n",
    "                # image_rgb -= image_rgb.min()\n",
    "                image_rgb /= image_rgb.max()\n",
    "            else:\n",
    "                hist = np.zeros((binsx, binsy, self.opt.nframe))\n",
    "                for i_frame in trange(self.opt.nframe):\n",
    "                    xv, yv = self.transform(z[:, :, i_frame])\n",
    "                    hist_, edge_x, edge_y = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                        bins=[binsx, binsy],\n",
    "                                                        range=[[0, 1], [0, self.ratio]],\n",
    "                                                        density=True)\n",
    "                #hist /= hist.max()\n",
    "\n",
    "            # 2/ transform light into image:\n",
    "            fnames = []\n",
    "            for i_frame in range(self.opt.nframe):\n",
    "                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)\n",
    "                if self.opt.multispectral:\n",
    "                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), vmin=0, vmax=1)\n",
    "                else:\n",
    "                    if do_color:\n",
    "                        bluesky = np.array([0.268375, 0.283377]) # xyz\n",
    "                        sun = np.array([0.325998, 0.335354]) # xyz\n",
    "                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)\n",
    "                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram\n",
    "                        L1 = 1 - hist[:, :, i_frame]\n",
    "                        L2 = hist[:, :, i_frame]\n",
    "                        image_denom = L1 / bluesky[1] + L2 / sun[1]\n",
    "                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom\n",
    "                        image_y = (L1 + L2) / image_denom \n",
    "                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))\n",
    "                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)\n",
    "                        image_L = self.opt.min_lum + (1-self.opt.min_lum)* L2 ** .61803\n",
    "                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)\n",
    "\n",
    "                    else:\n",
    "                        ax.imshow(1-image_L, vmin=0, vmax=1)\n",
    "\n",
    "                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'\n",
    "                fig.savefig(fname, dpi=dpi)\n",
    "                fnames.append(fname)\n",
    "                plt.close('all')\n",
    "\n",
    "            if self.opt.nframe==1:\n",
    "                shutil.copyfile(fname, output_filename)\n",
    "                return output_filename\n",
    "            else:\n",
    "                if self.opt.ext == 'gif':\n",
    "                    return make_gif(output_filename, fnames, fps=self.opt.fps)\n",
    "                else:\n",
    "                    return make_mp4(output_filename, fnames, fps=self.opt.fps)\n",
    "\n",
    "    def show(self, output_filename, width=1024):\n",
    "        from IPython.display import HTML, Image, display\n",
    "        if self.opt.nframe==1:\n",
    "            display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))\n",
    "        else:\n",
    "            if self.opt.ext == 'gif':\n",
    "                return display(Image(url=output_filename, width=width))\n",
    "            else:\n",
    "                #import moviepy.editor as mpy\n",
    "                #return mpy.ipython_display(output_filename, width=width)\n",
    "                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858\n",
    "                opts = ' loop=\"1\" autoplay=\"1\" controls '\n",
    "                html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n",
    "                html.reload()\n",
    "                return display(html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# a simple caustics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## generating the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.864888Z",
     "iopub.status.busy": "2022-09-16T06:50:17.864663Z",
     "iopub.status.idle": "2022-09-16T06:50:19.896847Z",
     "shell.execute_reply": "2022-09-16T06:50:19.896285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5120, 5120, 1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.899518Z",
     "iopub.status.busy": "2022-09-16T06:50:19.899287Z",
     "iopub.status.idle": "2022-09-16T06:50:19.902454Z",
     "shell.execute_reply": "2022-09-16T06:50:19.902008Z"
    }
   },
   "outputs": [],
   "source": [
    "c = Caustique(opt)\n",
    "output_filename = c.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.904998Z",
     "iopub.status.busy": "2022-09-16T06:50:19.904782Z",
     "iopub.status.idle": "2022-09-16T06:50:19.908171Z",
     "shell.execute_reply": "2022-09-16T06:50:19.907731Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-02_caustique/caustique_8e660a68.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# exploring parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.910794Z",
     "iopub.status.busy": "2022-09-16T06:50:19.910587Z",
     "iopub.status.idle": "2022-09-16T06:50:19.913072Z",
     "shell.execute_reply": "2022-09-16T06:50:19.912580Z"
    }
   },
   "outputs": [],
   "source": [
    "N_scan = 9\n",
    "base = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## water depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 0.750 -> output_filename='2022-12-02_caustique/caustique_H_0.750_c623bc91.png' \n",
      "H = 0.892 -> output_filename='2022-12-02_caustique/caustique_H_0.892_2b4aed09.png' \n",
      "H = 1.061 -> output_filename='2022-12-02_caustique/caustique_H_1.061_8926a7b4.png' \n",
      "H = 1.261 -> output_filename='2022-12-02_caustique/caustique_H_1.261_fb74ff8b.png' \n",
      "H = 1.500 -> output_filename='2022-12-02_caustique/caustique_H_1.500_c46add50.png' \n",
      "H = 1.784 -> output_filename='2022-12-02_caustique/caustique_H_1.784_01b21eb2.png' \n",
      "H = 2.121 -> output_filename='2022-12-02_caustique/caustique_H_2.121_f0120ece.png' \n",
      "H = 2.523 -> output_filename='2022-12-02_caustique/caustique_H_2.523_3daab247.png' \n",
      "H = 3.000 -> output_filename='2022-12-02_caustique/caustique_H_3.000_7f8b13e2.png' \n"
     ]
    }
   ],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## refraction index variation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:21.644704Z",
     "iopub.status.busy": "2022-09-16T06:50:21.644457Z",
     "iopub.status.idle": "2022-09-16T06:50:23.391217Z",
     "shell.execute_reply": "2022-09-16T06:50:23.390608Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.010  -> output_filename='2022-12-02_caustique/caustique_variation_0.010_9080d591.png'\n",
      "variation = 0.017  -> output_filename='2022-12-02_caustique/caustique_variation_0.017_7d9a1327.png'\n",
      "variation = 0.028  -> output_filename='2022-12-02_caustique/caustique_variation_0.028_70e54f05.png'\n",
      "variation = 0.046  -> output_filename='2022-12-02_caustique/caustique_variation_0.046_b3a8e6c6.png'\n",
      "variation = 0.077  -> output_filename='2022-12-02_caustique/caustique_variation_0.077_1fe5e789.png'\n",
      "variation = 0.129  -> output_filename='2022-12-02_caustique/caustique_variation_0.129_b5dacf5f.png'\n",
      "variation = 0.215  -> output_filename='2022-12-02_caustique/caustique_variation_0.215_8de2366e.png'\n",
      "variation = 0.359  -> output_filename='2022-12-02_caustique/caustique_variation_0.359_9174f3ea.png'\n",
      "variation = 0.599  -> output_filename='2022-12-02_caustique/caustique_variation_0.599_1dcf7faf.png'\n"
     ]
    }
   ],
   "source": [
    "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.variation = variation_\n",
    "    c.opt.tag = f'{opt.tag}_variation_{variation_:.3f}'\n",
    "\n",
    "    output_filename = c.plot(z)\n",
    "    print(f'variation = {variation_:.3f}  -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## other variables on the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:23.394466Z",
     "iopub.status.busy": "2022-09-16T06:50:23.394219Z",
     "iopub.status.idle": "2022-09-16T06:50:23.686162Z",
     "shell.execute_reply": "2022-09-16T06:50:23.685512Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "======scale======\n",
      "scale=scale(default)*0.500=1.000E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_0.500_9d61ef59.png'\n",
      "scale=scale(default)*0.595=1.189E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_0.595_047707a2.png'\n",
      "scale=scale(default)*0.707=1.414E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_0.707_b464886a.png'\n",
      "scale=scale(default)*0.841=1.682E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_0.841_869005e1.png'\n",
      "scale=scale(default)*1.000=2.000E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_1.000_73e1260e.png'\n",
      "scale=scale(default)*1.189=2.378E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_1.189_7fb554c9.png'\n",
      "scale=scale(default)*1.414=2.828E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_1.414_ceb3311f.png'\n",
      "scale=scale(default)*1.682=3.364E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_1.682_a70fc342.png'\n",
      "scale=scale(default)*2.000=4.000E+02 -> output_filename='2022-12-02_caustique/caustique_scale_modul_2.000_416eccaf.png'\n",
      "======B_sf======\n",
      "B_sf=B_sf(default)*0.500=1.250E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_0.500_a2b93b2b.png'\n",
      "B_sf=B_sf(default)*0.595=1.487E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_0.595_f205c5dd.png'\n",
      "B_sf=B_sf(default)*0.707=1.768E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_0.707_3f69f079.png'\n",
      "B_sf=B_sf(default)*0.841=2.102E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_0.841_9cd11c99.png'\n",
      "B_sf=B_sf(default)*1.000=2.500E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_1.000_bcde0799.png'\n",
      "B_sf=B_sf(default)*1.189=2.973E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_1.189_68999fb7.png'\n",
      "B_sf=B_sf(default)*1.414=3.536E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_1.414_4545bbf5.png'\n",
      "B_sf=B_sf(default)*1.682=4.204E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_1.682_08416e6d.png'\n",
      "B_sf=B_sf(default)*2.000=5.000E-01 -> output_filename='2022-12-02_caustique/caustique_B_sf_modul_2.000_6c6900a3.png'\n",
      "======theta======\n",
      "theta=theta(default)*0.500=1.200E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_0.500_7c58aaf8.png'\n",
      "theta=theta(default)*0.595=1.427E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_0.595_a1420462.png'\n",
      "theta=theta(default)*0.707=1.697E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_0.707_ccada2ea.png'\n",
      "theta=theta(default)*0.841=2.018E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_0.841_908de90c.png'\n",
      "theta=theta(default)*1.000=2.400E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_1.000_b9ee616d.png'\n",
      "theta=theta(default)*1.189=2.854E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_1.189_a59bcb48.png'\n",
      "theta=theta(default)*1.414=3.394E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_1.414_cc1cf9b5.png'\n",
      "theta=theta(default)*1.682=4.036E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_1.682_b6898cb1.png'\n",
      "theta=theta(default)*2.000=4.800E+00 -> output_filename='2022-12-02_caustique/caustique_theta_modul_2.000_ec23848e.png'\n",
      "======B_theta======\n",
      "B_theta=B_theta(default)*0.500=1.047E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_0.500_dea9b577.png'\n",
      "B_theta=B_theta(default)*0.595=1.245E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_0.595_a6fb9fac.png'\n",
      "B_theta=B_theta(default)*0.707=1.481E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_0.707_1407ba50.png'\n",
      "B_theta=B_theta(default)*0.841=1.761E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_0.841_1a1399cd.png'\n",
      "B_theta=B_theta(default)*1.000=2.094E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_1.000_d759e101.png'\n",
      "B_theta=B_theta(default)*1.189=2.491E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_1.189_3cf46bbc.png'\n",
      "B_theta=B_theta(default)*1.414=2.962E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_1.414_4f8a78da.png'\n",
      "B_theta=B_theta(default)*1.682=3.522E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_1.682_c736862c.png'\n",
      "B_theta=B_theta(default)*2.000=4.189E+00 -> output_filename='2022-12-02_caustique/caustique_B_theta_modul_2.000_2083b71f.png'\n",
      "======gamma======\n",
      "gamma=gamma(default)*0.500=1.400E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_0.500_5e9e1bd0.png'\n",
      "gamma=gamma(default)*0.595=1.665E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_0.595_c1d42567.png'\n",
      "gamma=gamma(default)*0.707=1.980E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_0.707_3acd5bac.png'\n",
      "gamma=gamma(default)*0.841=2.355E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_0.841_5af611f4.png'\n",
      "gamma=gamma(default)*1.000=2.800E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_1.000_16a8cfe4.png'\n",
      "gamma=gamma(default)*1.189=3.330E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_1.189_f36eb09d.png'\n",
      "gamma=gamma(default)*1.414=3.960E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_1.414_47657a56.png'\n",
      "gamma=gamma(default)*1.682=4.709E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_1.682_590126f2.png'\n",
      "gamma=gamma(default)*2.000=5.600E+00 -> output_filename='2022-12-02_caustique/caustique_gamma_modul_2.000_22d9c2bd.png'\n"
     ]
    }
   ],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', ]: #  'V_Y', 'V_X', 'B_V', \n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = init()\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        \n",
    "        z = c.wave()\n",
    "        output_filename = c.plot(z)\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
    "        if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a grid image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_image(nx, ny, periods=6.5, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    image = (image>=1) * 1.\n",
    "    image *= ((X**2 + Y**2) < radius**2) * 1.\n",
    "    return image\n",
    "image = grid_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=0.45, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-02_caustique/caustique_grid-image_b9f678bc.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_grid-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2022-12-02_caustique/caustique_grid-image_b9f678bc.png'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output_filename"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.100 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.100_c8729206.png' \n",
      "threshold=0.200 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.200_0fedc588.png' \n",
      "threshold=0.300 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.300_38f8719f.png' \n",
      "threshold=0.400 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.400_7d2fccf4.png' \n",
      "threshold=0.500 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.500_3d9f0e2b.png' \n",
      "threshold=0.600 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.600_e5a2a9f6.png' \n",
      "threshold=0.700 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.700_be1dce2e.png' \n",
      "threshold=0.800 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.800_2dd5dc05.png' \n",
      "threshold=0.900 -> output_filename='2022-12-02_caustique/caustique_grid-image_threshold=0.900_7c27134d.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grid-image_{threshold=:.3f}'\n",
    "    image = grid_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=1.000_d8c6a205.png'\n",
      "periods=1.334 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=1.334_2af9e43b.png'\n",
      "periods=1.778 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=1.778_0f0269a6.png'\n",
      "periods=2.371 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=2.371_709551d9.png'\n",
      "periods=3.162 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=3.162_914dc7c9.png'\n",
      "periods=4.217 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=4.217_fa6a3f7b.png'\n",
      "periods=5.623 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=5.623_d2c0ab7f.png'\n",
      "periods=7.499 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=7.499_6ebb3a96.png'\n",
      "periods=10.000 -> output_filename='2022-12-02_caustique/caustique_grid-image_periods=10.000_70589b19.png'\n"
     ]
    }
   ],
   "source": [
    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grid-image_{periods=:.3f}'\n",
    "    image = grid_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods, threshold=.2)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{periods=:.3f} -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a square image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_image(nx, ny,  radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = grid_image(nx=c.opt.nx, ny=c.opt.ny, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-02_caustique/caustique_square-image_26e88b3c.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_square-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius = 0.000 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.000_29152b8c.png'\n",
      "radius = 0.125 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.125_40934c5d.png'\n",
      "radius = 0.250 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.250_aa7a2b08.png'\n",
      "radius = 0.375 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.375_c27b45b8.png'\n",
      "radius = 0.500 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.500_2c1fc07a.png'\n",
      "radius = 0.625 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.625_ed1e431c.png'\n",
      "radius = 0.750 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.750_fc2a1988.png'\n",
      "radius = 0.875 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=0.875_27b759a8.png'\n",
      "radius = 1.000 -> output_filename='2022-12-02_caustique/caustique_square-image_radius=1.000_b963a758.png'\n"
     ]
    }
   ],
   "source": [
    "for radius in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_square-image_{radius=:.3f}'\n",
    "    image = grid_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'radius = {radius:.3f} -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  }
 ],
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