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Fractals

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En esta aplicación creamos una imagen de forma procedimental calculando el color de cada píxel mediante algoritmos fractales (Figura 1). Algunos de los resultados más fascinantes producidos por un sistema dinámico se dan cuando iteramos una función de variable compleja en lugar de real. Este es el caso de los conjuntos de Julia. El código fuente está en la caperta /src/demo/fractals de la distribución del SDK.

Captura de un visor de conjuntos de Julia, versión Windows. Captura de un visor de conjuntos de Julia, versión macOS.
Figura 1: Aplicación Fractals versión Windows y macOS.
Captura de un visor de conjuntos de Julia, versión Linux/Ubuntu. Captura de un visor de conjuntos de Julia, versión Raspbian.
Figura 2: Versión Ubuntu y Raspbian.

Debido a la gran carga computacional de este algoritmo hemos dividido el cálculo en varios hilos (Figura 3). Este problema es fácilmente paralelizable simplemente fraccionando la imagen, gracias a que cada píxel se obtiene de forma independiente.

Imagen dividida en cuatro partes y cuatro hilos de ejecución calculando cada una.
Figura 3: Colaboración de varios hilos de ejecución.
Listado 1: demo/fractals/fractals.c
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/* Multi-threaded fractals */

#include <nappgui.h>

typedef struct _app_t App;
typedef struct _thdata_t ThData;

struct _app_t
{
    Window *window;
    ImageView *view;
    Label *time_label;
    Clock *clock;
    uint32_t threads;
    bool_t vertical;
    real64_t fct;
};

struct _thdata_t
{
    real64_t fct;
    real64_t kreal;
    real64_t kimag;
    Pixbuf *pixbuf;
    uint32_t i;
    uint32_t j;
    uint32_t width;
    uint32_t height;
};

static const real64_t i_FCT = 2.85;
static const uint32_t i_ITERATIONS = 512;
static const uint32_t i_WIDTH = 601;
static const uint32_t i_HEIGHT = 601;

/*---------------------------------------------------------------------------*/

static uint32_t i_inset(real64_t zreal, real64_t zimag, real64_t creal, real64_t cimag)
{
    uint32_t i;
    for(i = 0; i < i_ITERATIONS; ++i)
    {
        real64_t ztmp, zdist;
        ztmp = zreal * zreal - zimag * zimag;
        zimag = zreal * zimag + zreal * zimag;
        zreal = ztmp;
        zreal = zreal + creal;
        zimag = zimag + cimag;
        zdist = zimag * zimag  + zreal * zreal;
        if (zdist > 3)
            return i;
    }

    return 0;
}

/*---------------------------------------------------------------------------*/

static uint32_t i_julia_thread(ThData *data)
{
    real64_t fct = data->fct;
    uint32_t imgwidth = pixbuf_width(data->pixbuf);
    real64_t freal = fct / imgwidth;
    real64_t fimag = fct / pixbuf_height(data->pixbuf);
    real64_t kreal = data->kreal;
    real64_t kimag = data->kimag;
    uint32_t val;
    real64_t creal, cimag;
    uint32_t stj = data->j;
    uint32_t edj = data->j + data->height;
    uint32_t sti = data->i;
    uint32_t edi = data->i + data->width;
    uint32_t i, j;

    for(j = stj; j < edj; ++j)
    {
        cimag = fimag * j - (fct / 2);

        for(i = sti; i < edi; ++i)
        {
            creal = freal * i - (fct / 2);
            val = i_inset(creal, cimag, kreal, kimag);
            if (val > 0)
            {
                uint8_t n_val = (uint8_t)(val % 255);
                if ( val < ( i_ITERATIONS >> 1 ) )
                    val = color_rgb((uint8_t)(n_val << 2), (uint8_t)(n_val << 3), (uint8_t)(n_val << 4));
                else
                    val = color_rgb((uint8_t)(n_val << 4), (uint8_t)(n_val << 2), (uint8_t)(n_val << 5));
            }
            else
            {
                val = kCOLOR_BLACK;
            }

            pixbuf_set(data->pixbuf, i, j, val);
        }
    }

    return 5;
}

/*---------------------------------------------------------------------------*/

static void i_julia(const uint32_t nthreads, const bool_t vertical, const real64_t fct, const real64_t kreal, const real64_t kimag, Pixbuf *pixbuf)
{
    ThData data[8];
    uint32_t width = pixbuf_width(pixbuf);
    uint32_t height = pixbuf_height(pixbuf);
    data[0].fct = fct;
    data[0].kreal = kreal;
    data[0].kimag = kimag;
    data[0].pixbuf = pixbuf;

    if (nthreads == 1)
    {
        data[0].i = 0;
        data[0].j = 0;
        data[0].width = width;
        data[0].height = height;
        i_julia_thread(&data[0]);
    }
    else
    {
        Thread *thread[8];

        uint32_t i;
        if (vertical == TRUE)
        {
            uint32_t twidth = width / nthreads;
            for (i = 0; i < nthreads; ++i)
            {
                data[i] = data[0];
                data[i].i = i * twidth;
                data[i].j = 0;
                data[i].width = twidth;
                data[i].height = height;
            }

            data[nthreads-1].width += (width - (twidth * nthreads));
        }
        else
        {
            uint32_t theight = height / nthreads;
            for (i = 0; i < nthreads; ++i)
            {
                data[i] = data[0];
                data[i].i = 0;
                data[i].j = i * theight;
                data[i].width = width;
                data[i].height = theight;
            }

            data[nthreads-1].height += (height - (theight * nthreads));
        }

        for (i = 0; i < nthreads; ++i)
            thread[i] = bthread_create(i_julia_thread, &data[i], ThData);

        for (i = 0; i < nthreads; ++i)
        {
            uint32_t thid = bthread_wait(thread[i]);
            cassert_unref(thid == 5, thid);
            bthread_close(&thread[i]);
        }
    }
}

/*---------------------------------------------------------------------------*/

static void i_image(App *app)
{
    Pixbuf *pixbuf = pixbuf_create(i_WIDTH, i_HEIGHT, ekRGBA32);
    real64_t rfactor = app->fct / i_WIDTH;
    real64_t ifactor = app->fct / i_HEIGHT;
    real64_t kreal = rfactor * 307 - 2;
    real64_t kimag = ifactor * 184 - 1.4;
    Image *image = NULL;
    real64_t timems;
    String *str;
    clock_reset(app->clock);
    i_julia(app->threads, app->vertical, app->fct, kreal, kimag, pixbuf);
    timems = 1000. * clock_elapsed(app->clock);
    str = str_printf("%.3f milliseconds", timems);
    label_text(app->time_label, tc(str));
    str_destroy(&str);
    image = image_from_pixbuf(pixbuf, NULL);
    imageview_image(app->view, image);
    image_destroy(&image);
    pixbuf_destroy(&pixbuf);
}

/*---------------------------------------------------------------------------*/

static void i_OnSlider(App *app, Event *e)
{
    const EvSlider *p = event_params(e, EvSlider);
    real64_t st = i_FCT - 1;
    real64_t ed = i_FCT + 1;
    app->fct = ((ed - st) * p->pos) + st;
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static void i_OnThreads(App *app, Event *e)
{
    const EvButton *p = event_params(e, EvButton);
    switch(p->index) {
    case 0: app->threads = 1; break;
    case 1: app->threads = 2; break;
    case 2: app->threads = 3; break;
    case 3: app->threads = 4; break;
    case 4: app->threads = 8; break; }
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static void i_OnVertical(App *app, Event *e)
{
    const EvButton *p = event_params(e, EvButton);
    app->vertical = p->index == 0 ? TRUE : FALSE;
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static Panel *i_panel(App *app)
{
    Panel *panel = panel_create();
    Layout *layout1 = layout_create(1, 3);
    Layout *layout2 = layout_create(5, 1);
    Label *label1 = label_create();
    Label *label2 = label_create();
    PopUp *popup = popup_create();
    Slider *slider = slider_create();
    Button *button1 = button_radio();
    Button *button2 = button_radio();
    ImageView *view = imageview_create();
    label_text(label1, "Threads:");
    popup_add_elem(popup, "1", NULL);
    popup_add_elem(popup, "2", NULL);
    popup_add_elem(popup, "3", NULL);
    popup_add_elem(popup, "4", NULL);
    popup_add_elem(popup, "8", NULL);
    popup_selected(popup, 0);
    popup_OnSelect(popup, listener(app, i_OnThreads, App));
    slider_value(slider, .5f);
    slider_OnMoved(slider, listener(app, i_OnSlider, App));
    button_text(button1, "Vert");
    button_text(button2, "Hotz");
    button_state(button1, ekGUI_ON);
    button_OnClick(button1, listener(app, i_OnVertical, App));
    imageview_size(view, s2di(i_WIDTH, i_HEIGHT));
    layout_slider(layout1, slider, 0, 0);
    layout_label(layout2, label1, 0, 0);
    layout_popup(layout2, popup, 1, 0);
    layout_button(layout2, button1, 2, 0);
    layout_button(layout2, button2, 3, 0);
    layout_label(layout2, label2, 4, 0);
    layout_halign(layout2, 4, 0, ekJUSTIFY);
    layout_hexpand(layout2, 4);
    layout_layout(layout1, layout2, 0, 1);
    layout_imageview(layout1, view, 0, 2);
    layout_vmargin(layout1, 1, 5);
    layout_margin2(layout2, 0, 5);
    layout_hmargin(layout2, 0, 5);
    layout_hmargin(layout2, 1, 10);
    layout_hmargin(layout2, 2, 5);
    layout_hmargin(layout2, 3, 15);
    panel_layout(panel, layout1);
    app->fct = i_FCT;
    app->threads = 1;
    app->vertical = TRUE;
    app->view = view;
    app->time_label = label2;
    return panel;
}

/*---------------------------------------------------------------------------*/

static void i_OnClose(App *app, Event *e)
{
    osapp_finish();
    unref(app);
    unref(e);
}

/*---------------------------------------------------------------------------*/

static App *i_create(void)
{
    App *app = heap_new0(App);
    Panel *panel = i_panel(app);
    app->window = window_create(ekWINDOW_STD);
    app->clock = clock_create(0);
    i_image(app);
    window_panel(app->window, panel);
    window_title(app->window, "Fractals");
    window_origin(app->window, v2df(500, 200));
    window_OnClose(app->window, listener(app, i_OnClose, App));
    window_show(app->window);
    return app;
}

/*---------------------------------------------------------------------------*/

static void i_destroy(App **app)
{
    window_destroy(&(*app)->window);
    clock_destroy(&(*app)->clock);
    heap_delete(app, App);
}

/*---------------------------------------------------------------------------*/

#include "osmain.h"
osmain(i_create, i_destroy, "", App)
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